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FOR 1940 









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(with A. N. Whitehead) 













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{John Lane) 









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for the purposes of private study, research^ 
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This book has developed gradually over a period of years 
culminating in a series of academic appointments. In 1938 
treated part of the subject in a course of lectures on "Language 
and Fact" at the University of Oxford. These lectures formed 
the basis for seminar courses at the University of Chicago in 
1938-9 and the University of California at Los Angeles in 
1939-40. The discussions at the two seminars did much to 
widen my conception of the problems involved and to diminish 
the emphasis wldch I originaJly placed on the linguistic aspects 
of the subject. I have to express a collective obligation to those 
both Professors and pupils, who, by detailed friendly criticism 



helped (I hope) in the avoidance of errors and fallacies. More 
especially at Chicago, where the seminar was often attended by 
Professors Camap and Morris, and where some of the graduate 
students showed great philosophic ability, the discussions were 
models of fruitful argumentative cooperation. Mr. Norman 
Dalkey, who attended both seminars, has since read the whole 

book in manuscript, and I am gready indebted to him for his 
careful and stimulating criticism. Finally, during the summer of 

1940, I prepared these William James Lectures partly from 
accumulated material, and partly from a re-consideration of the 
whole subject. 

As will be evident to the reader, I am, as regards method, 
more in sympathy with the logical^positivists than with any other 
existing school. I differ from them, however, in attaching more 
importance than they do to the work of Berkeley and Hume. 
The book results from an attempt to combine a general outlook 
akin to Hume's with the methods that have grown out of modem 





What is a Word ? 







If. Sentences, Syntax, and Parts of Speech 30 

III. Sentences Describing Experiences 48 

IV. The Object-Language 

V. Logical Words 

VI» Proper Names 

Vn. Egocentric Particulars 

VIII . Perception and Knowledge 

IX. Epistemological Premisses 

X. Basic Propositions 

XI. Factual Premisses 




\^/^II. An Analysis of Problems Concerning Propositions 1 66 

XIII. The Significance of Sentences: A. General. 

B. Psychological. C. Syntactical 170 

XIV. Language as Expression 
XV. What Sentences "Indicate" 



XVI. Truth and Falsehood, Preliminary Discussion zi6 

XVII. Truth and Experience 

XVIII. General Beliefs 

XIX. Extensionality and Atomicity 

XX. The Law of Excluded Middle 

XXL Truth and Verification 

XXII. Significance and Verification 

XXIII. Warranted Assertibility 

XXIV. Analysis 

XXV. . Language and Metaphysics 











The present work is intended as an investigation of certain 
problems concerning empirical knowledge. As opposed to tradi- 
tional theory of knowledge, the method adopted differs chiefly 
in the importance attached to linguistic considerations • I propose 
to consider language in relation to two main problems, which, in 
preliminary and not very precise terms, may be stated as follows : 

. What is meant by "empirical evidence for the truth of a 


II. What can be inferred from the fact that there sometimes is 

such evidence .^ 

Here, as usually in philosophy, the first difficulty is to see 
that the problem is difficult. If you say to a person untrained 


in philosophy, "How do you know I have two eyes?" he or 


she will reply, "What a silly question! I can see you Iiave.'* 
It is not to be supposed that, when our inquiry is finished, we 
shall have arrived at anything radically different from this un- 
philosophical position. What will have happened will be that 
we shall have come to see a complicated structure where we 
thought everything was simple, that we shall have become aware 
of the penumbra of uncertainty surrounding the situations whicln 
inspire no doubt, that we shall find doubt more frequently 
justified than we supposed, and that even the most plausible 
premisses will have shown themselves capable of yielding un- 
plausible conclusions. The net result is to substitute articulate 
hesitation for inarticulate certainty. Whether this result has any 
value is a question which I shall not consider. 

As soon as we take our two questions seriously, difiiculties 
crowd upon us. Take the phrase "empirical evidence for the 
truth of a proposition". This phrase demands that we should 
define the words "empirical", "evidence", "truth", "proposition", 
unless we conclude, after examination, that our question has been 
wrongly worded. 




Let US begin with "proposition". A proposition is something 
which may be said in any language: "Socrates is mortal" and 
"Socrate est mortel" express the same proposition. In a given 
language it may be said in various ways : the difference between 

Caesar was killed on the Ides of March 


Ides of March that Caesar was killed 

"it was on the 

is merely rhetorical 

is thus possible for tsvo forms of words to "have the same 




may. at least for the moment 




a "pro 


as some given sentence 
We must now define 

all the sentences which have the same meaning 




"having the same 
meaning". Ignoring the latter for the moment, what is a sentence? 
may be a single word, or, more usually, a number of words 
put together according to the laws of syntax; but what dis- 
tinguishes it is that it expresses something of the nature of an 
assertion, a denial, an imperative, a desire, or a question. What 
is more remarkable about a sentence, from our point of view 
is that we can understand what it expresses if we know the 
meaning of its several words and the rules of syntax. Our in- 
vestigation must therefore begin with an examination first of 
words, and then of syntax. 

Before entering upon any detail, a few general remarks as to 
the nature of our problem may help us to know what is relevant. 

Our problem is one in the theory of knowledge. What is die 
theory of knowledge ? Everything that we know, or think we 
know, belongs to some special science; what, then, is left over 
for theory of knowledge 


There are two different inquiries, both important, and each 
having a right to the name "theory of knowledge". In any given 
discussion, it is easy to fall into confusions through failure to 
determine to which of the two inquiries the discussion is intended 
to belong. I will therefore, at the outset, say a few words in 
explanation of both. 

In the first form of theory of knowledge, we accept the scien- 
tific account of the world, not as certainly true, but as the best 
at present available. The world, as presented by science, contains 





a phenomenon called "knowing", and theory of knowledge, in 
its first form, has to consider what sort of phenomenon this is. 
Viewed from the outside, it is, to begin with, a characteristic 
of living organisms, which is (broadly speaking) increasingly 
displayed as the organism becomes more complex. It is clear that 
knowing is a relation of the organism to something else or to 
a part of itself. Still taking an outside observer's point of view 
we may distinguish perceptive awareness from habit-knowledge. 
Perceptive awareness is a species of "sensitivity", which is not 
confined to living organisms, but is also displayed by scientific 
instruments, and to some degree by everything. Sensitivity con- 
sists in behaving, in the presence of a stimulus of a certain kind 
in a way in which the animal or thing does not behave in its 

A cat has a characteristic behaviour in the presence of a dog; 

this makes us say that the cat "perceives" the dog. But a gal- 
vanometer has a characteristic behaviour in the presence of an 
electric current, and yet we do not say that it "perceives" the 
electric current. The difference between the two cases has to do 
with "habit-knowledge". 

An inanimate thing, so long as its physical constitution 
remains unchanged, makes always the same response to the same 
stimulus. An animal, on the contrary, when presented repeatedly 
with a stimulus to which, from the first, it makes some response 
will gradually alter the character of the response until it reaches 
a point of (at least temporary) stability. When this point has been 
reached, the animal has acquired a "habit". Every habit involves 
what, from a behaviourist point of view, might count as belief 
in a general law, or even (in a sense) as knowledge of such a law 
if the belief happens to be true. For example, a dog that has 
learnt to sit up and beg for food might be said by a behaviourist 
to believe the general law: "the smell of food plus begging is 
followed by food; the smell of food alone is not". 

What is called "learning by experience", which is characteristic 
of living organisms, is the same thing as the acquisition of habits. 

dog learns by experience that human beings can open doors 






and therefore, if his master is present when he wants to go out, 
barks round him instead of scratching at the doon "Signs" depend 
as a rule, upon habits learnt by experience. His master's voice 
is, to a dog, a sign of the master. We may say that A is a **sign 



of B if it promotes behaviour that B would promote, but that 
has no appropriateness to A alone. It must be admitted, howeve 


that some signs are not dependent upon experience for their 
efficacy; animals respond to certain smells in a manner appro- 

priate to the objects emitting the smells^ and sometimes can do 
so even when they have never experienced the objects in question. 
The precise definition of a "sign'* is difficult, both on this account, 
and because there is no satisfactory definition of '^appropriate'* 
behaviour- But the general character of what is meant is fairly 
clear, and it will be seen that language is a species of the genus 

signs, it is possible to trace the beginnings of the distinction 
between "subjective'* and **objective**, and also between **know- 
ledge" and **error**. Subjectively, A is a sign of B for an organism 

if O behaves in the presence of A in a manner 

to B, Objectively, A is a sign of B if, in fact, A is accompanied 

or followed by B, Whenever A is subjectively a sign of B for the 

organism O, we may say that, speaking behaviouristically, 

**believes'* the general proposition **A is always accompanied 
or followed by B**, but this belief is only **true** if A is objectively 
a sign of B* Animals can be deceived by mirrors or scents. Such 

instances make it clear that, from our present point of view 


the distinctions ''subjective-objective*' and **knowledfi:e-error** 
begin at a very early stage in animal behaviour* Both knowledge 


and error, at this stage, are observable 

behaviour of the organism and the facts of the environment. 

Within its limitations, theory of knowledge of the above sort 
is legitimate and important* But there is another kind of theory 
of knowledge which goes deeper and has, I think^ much greater 

When the behaviourist observes the doings of animtals^ and 



decides whedier these show knowledge or error, he is not 
thinking of himself as an animal, but as an at least hypothetically 
inerrant recorder of what actually happens. He **knows'' that 

animals are deceived by mirrors, and believes himself to *'know' 
that he is not being similarly deceived. By omitting the fact that 
he — ^an organism like any other — ^is observing, he gives a false 


air of objectivity to the results of his observation. As soon 
we remember the possible fallibility of the observer, we have 
introduced the serpent into the behaviourist*s paradise* The 
serpent whispers doubts, and has no difficulty in quoting scien- 
tific scripture for the purpose. 

Scientific scripture, in its most canonical form, is embodied 
in physics (including physiology). Physics assures us that the 
occurrences which we call "perceiving objects" are at the end 
of a long causal chain which starts from the objects, and are not 
likely to resemble the objects except, at best, in certain very 
abstract ways. We all start from "naive realism'', i.e., the doctrine 
that things are what they seem. We think that grass is green, 
that stones are hard, and that snow is cold. But physics assures 
us that the greenness of grass, the hardness of stones, and the 
coldness of snow, are not the greenness, hardness, and coldness 
that we knpw in our own experience, but something very dif- 
ferent. The observer, when he seems to himself to be observing 
a stone, is really, if physics is to be believed, observing the effects 
of the stone upon himself. Thus science seems to be at war with 
itself: when it most means to be objective, it finds itself plunged 
into subjectivity against its will. Naive realism leads to physics, 
and physics, if true, shows that naive realism is false 
naive realism, if true, is false : therefore it is false. And 

, *j. ..^v*^, *« *-*.^^, 

the behaviourist, when he thinks he is recording observations 
about the outer world, is really recording observations about 

wh„ n happ«^ng in him ' 

These considerations induce doubt, and therefore lead us to 
a critical scrutiny of what passes as knowledge. This 
scrutiny is "theory of knowledge'* in the second of the two 
senses mentioned 2i)0ve, or "epistemology", as it is also called. 



The first step in such a scrutiny is the arrangement of what 
we think we know in a certain order, in which what comes later 
is known (if it is known) because of what comes earlier. This 
conception, however, is not so clear as it might seem to be. 
is not identical with logical order, nor yet with order of dis- 
covery, though it has connections with both. Let us illustrate 
by some examples. 

In pure mathematics, after the elements, logical order and 
order of knowledge are identical. In a treatise (say) on Theory 
of Functions, we believe what the author says because he deduces 
it from simpler propositions which are already believed; that 

is to say, the cause of our beliefs is also their logical ground. 
But this is not true at the beginning of mathematics. Logicians 
have reduced the necessary premisses to a very small number 
of highly abstract symbolic propositions, which are difEcult to 
understand, and which the logicians themselves only believe 
because they are found to be logically equivalent to a large num- 
ber of more familiar propositions- The fact that mathematics can 
be deduced from these premisses is emphatically not the reason 
for our belief in the truth of mathematics. 

What epistemology requires of mathematics, though it is not 
the logical order, is also not the psychological cause of our 

beliefs. Why do you believe that 7 X 8 = 56 .^ Have you ever 

verified this proposition.^ Certainly I never have. I believe it 
because I was told it in childhood, and have since seen it repeated 

by reputable authors. But when I am engaged in an epistemo 
logical investigation of mathematical knowledge, I ignore these 

historical causes of my belief that 7 X 8 = 56. The problem for 
epistemology is not *Vhy do I believe this or that?" but "why 
shotdd I believe this or that?" In fact, the whole subject is a 

product of Cartesian doubt. I observe that men err, and I ask 

myself what I must do to avoid error. Obviously one thing 

that I must do is to reason correctly, but I must also have 
premisses from which to reason. In a perfected epistemology, 
the propositions will be arranged in a logical order, though not 
in the logical order that a logician would prefer. 






J ^ 


Take the case of astronomy. In the mathematical theory of 
planetary motions, the logical order starts from the law of 
gravitation, but the historical order starts from the observations 
of Tycho Brahe, which led to Kepler's Laws. The epistemological 
order is similar to the historical order, but not identical since 

, *^**.. **ww *^^«..x^**x, 

we cannot be content with old observations. If we are to use 
them, we must first find evidence of their trustworthiness* which 


we can only do by means of observations of our own. 

Or, again, take history. If there were a science of history, 
its facts would be deduced from general laws, which would come 
first in the logical order. In the epistemological order, most of 
us are content to believe, about (say) Julius Caesar, what we find 
in reliable books. But the critical historian must go to manuscripts 
and inscriptions; his data are certain shapes, of which the inter- 
pretation may sometimes be very difficult. In the case of cunei- 
form inscriptions, for example, the interpretation depends upon 
very elaborate inductions ; to set out why we should believe what 
we do about Hamurabi is a complicated matter. For the critical 
historian, the essential premisses are that he sees certain shapes 
on certain tablets; for us, that he says he does, together with 
whatever reasons we may have for believing him to be truthful, 
which must consist in a comparison of his statements with our 


own experiences. # 

Epistemology must arrange all our beliefs, both those of which 
we feel convinced, and those that seem to us only more or less 
probable, in a certain order, beginning with those that, on 
reflection, appear to us credible independently of any argument 
in their favour, and indicating the nature of the inferences (mostly 
not strictly logical) by which we pass from these to derivative 
beliefs. Those statements about matters of fact that appear 
credible independently of any argument in their favour may be 
called "basic propositions*'.* These are connected with certain 
non-verbal occurrences which may be called "experiences"; the 
nature of this connection is one of the fundamental questions 
of epistemology. 


This is the expression used by Mr, Ay 





Epistemology involves both logical and psychological ele- 
ments* Logically, we have to consider the inferential relation 
(usually not that of strict deduction) between basic propositions 
and diose that we believe because of them; also the logical 
relations which often subsist between different basic propositions, 
causing them, if we accept certain general principles, to fit into 
a system which, as a whole, strengthens the probability of each 
of its constituents; also the logical character of basic proposi- 
tions themselves. Psychologically, we have to examine the rela- 
tion of basic propositions to experiences, the degree of doubt 
or certainty that we feel in regard to any of them, and the methods 
of diminishing the former and increasing the latter. 

I shall, throughout this book, try to avoid the consideration 
of logical and mathematical knowledge, which does not raise the 
problems that I wish to discuss. My main problem, throughout, 
will be the relation of basic propositions to experiences, i,e., of 
the propositions that come first in the epistemological order to 
the occurrences which, in some sense, are our grounds for 
accepting these propositions* 

The subject with which I shall be concerned is different from 
that discussed, for instance, in Carnap's Loffjcd Syntax 
Language^ though at many points the discussions in that book 

and others dealing with similar topics are relevant. I am con- 
cerned with what makes empirical propositions true, and with 
the definition of **truth" as applied to such propositions. Empiri- 
cal propositions, except when their subject-matter happens to be 
linguistic, are true in virtue of occurrences which are not lin- 
guistic. In considering empirical truth^ therefore, we are concerned 
with a relation between linguistic and non-linguistic events, or 
rather, with a series of relations of gradually increasing com- 
plexity. When we see a shooting star and say "look**, the relation 
is simple; but the relation of the law of gravitation to the obser- 
vations upon which it is based is exceedingly complex* 

Empiricism, in agreement with common sense, holds that a 
verbal statement may be confirmed or confuted by an observation, 
provided it is a statement which is significant and is not one of 



logic. Now the "observation", in such a case, is supposed to 

be something non-verbal which we "experience**. But if an 
observation is to confirm or confute a verbal statement, it must 
itself give ground, in some sense, for one or more verbal state- 
ments. The relation of a non-verbal experience to a verbal state- 
ment which it justifies is thus a matter which empiricism is bound 

to investigate. 
The general course of my argument will be as follows. 

In the first three chapters, I am concerned with an informal 
and introductory discussion of words, sentences, and the relation 
of an experience to a sentence which (partially) describes it* One 
of the difficulties of the subject is that we have to use common 
words in precise technical senses which they do not commonly 

bear; in these opening chapters, I have avoided such technical 
definitions, while preparing the ground for them by showing 


the nature of the problem for the sake of which they are needed 
What is said in these chapters, accordingly, has not the degree 
of precision sought in later chapters. 

Chapters IV-VII are concerned with certain problems in the 
analysis of language. One of the results that have emerged most 
clearly from the logical study of language is, that there must be 
a hierarchy of languages, and that the words "true" and "false 
as applied to the statements in any given language, are them 
selves words belonging to a language of higher order. This 
entails, as a consequence, the existence of a language of lowest 
order, in which the words "true" and "false" do not occur. So 
far as logical considerations are concerned, this language might 

be constructed in many waysj its syntax and vocabulary are not 


determined by the logical conditions, except that it should not 
allow apparent variables, i.e., it should not contain the words 
"all" and "some". Proceeding psychologically, I construct a 
language (not the language) fulfilling the logical conditions for 

the language of lowest type; I call this the "object-language" or 
the "primary language". In diis language, every word "denotes" 

or means" a sensible object or set of such objects, and, when 
used alone, asserts the sensible presence of the object, or of one of 



the set af objects^ which if ckf^otts m nw^xm. In dctintng this 
anguagi% it is necessary ic^ tkfmv **denofing** or **nuuining'* as 
applkxl ta iibjc'ct-wards^ ue.^ to the Witnls «f this 
Words in bngtuij^c;* of higher uttkt^ ''mean' in m\wr mul much 
more coimplicaicd \%'av^. 


We p%is?; fnnn the priniury ft* t\w siXinuhty language 
adding what 1 call *1<>gic4l words*\ such as **ar*\ '*mn*\ **scimt* 
am! **air\ lo^^ilitT with die wvtrds **uue'* and *1a!stf'' as applied 
10 Hentences in die cibjecf-bnpiage. The developineni of bn- 

*f higher arder thm du* secand in ii miif rer ht die logician^ 
•iiince it raises tm new prt^hlem^ an li* die rehitian between sim* 
tencen ;uid m'iri-Iin|jiii:sfic tKcurrences* 

iaprer?i VI imi Vlt ure c«jnc:erned with sytiiactieal tjuesiiun^^ 
y **pr«|XT names'* md **egi,»ceiiiric pariictdar^**'---i.r,^ wtird** 



such as **djiH*\ *T\ **m.nv*\ which have 4 ineaniitit relative lu 
fhe speaker. *rhe dieury u( pr^i^jH^r juiiu^ which is suj^gesied is 
iinpriruni if triu% in pariicwbr in cmmixtkm with spuce and time. 

m\t (urn chapters are eancerned widi |x*reepdve hum 
e, and tmrn* pariicidarly widi *''basic prupasiiians*\ i*e*^ widi 

those prapti?»idons which tnmt direedy repurf ktwwledge derived 
fram jx*reeptian. 

V aid thai if is die husiness «^f epi^ietnoluuv ttt arMnue die 

propcisidanii which cimsiimfe our knawledge in a certain It* 

order, m which die later priiposiiicnis are accepii*d bt*eause a 

dieir mmcm tiAmitm la dicise diat etiine k*fore dieKiL li is not 

nec«?ssary dwf ihc bier propcisiiiintj* shiiidd kf higically dedwcible 
from die earlier tmm: what is neceHsarv is diai the earlier tmm 

should supply whatever grauiids mi^t far ihinking it likely thai 

the later ones are true. When we are amsidering enrnpirica! kiKiw- 

e, the eariiesi prop0siii<ms in the hierarchy^ which give the 

rounds ht all the others, are t%m dtimei fram cnher prii|K»si 

lions, and yet are not mere arbitrary assumptttnis* They have 

roynds, diough their grounds are not, prcipmiiions^ bat tib- 

served occurrences* Such prdposiisons.^ as observed above^ I slial! 
cat! **basfc** prciposifions; ihey fulfd die functioo assigned by 

tlie logical pcisitivisis to what they call **pr«itocd prapfj«itions 





It is, to my mind, one of the defects of the logical positivisb 

that their linguistic bias makes their theory of protcxrol 
tions vague and unsatisfactory. 

We pass next to the analysis of **propositional attitudes**^ i*e* 
believing, desiring^ doubting^ etc*^ that so-and-so is the case 


Both for logic and for theory of knowledge, the analysis of such 
occurrences is important, especially in the case of belief. We find 

that believing a given proposition does not necessarily involve 
words, but requires only that the believer should he in one 
a number of possible states defined, mainly if not who 

When words occur> they *'express*' the l>elief 

and. if true* **indicate'* a fact other than tlic 

> '* **.-^> 



The theory of truth and falsehood which naturally re^uhs imm 

such considerations as I have ht^m su 


IS an epiJiiemo 

logical theory^ that is to say, it only affords a definition of **inie'* 
and "false" where there is some metlnid of obtaining such 

knowledge as would decide the alternative. This suggests Brouwer 

and his denial of the law of excluded middle* It accordingly 

becomes necessary to consider whether it is possible to give u 

non-epistemobgical definition of **trye*' and *1ake**^ and sri 

preserve the law of excluded middle. 
Finally there is the question; how far^ if at all, do ihe logka 

of language correspond to elements in the mm 

linguistic world that language deals with? Or^ in other words: 

does logic afford a basis for any metaphysical dt>ctrine ? In ?ipife 

of all that has been said by the logical posiiivi^its, 1 inctim* lu 

answer this question in the affirmative; but it is a difliculi maiirr 
as to which I have not the audacity to bcf dogmaiic 


There are three theses which I regard us sfxtcialty important 
in what follows* 

It is argued that^ on the basis of a ■^.inglc eKfK^riencr, a 
mmhet of verba! statements are justified. The character of ^mh 

is investigated^ and it is contended thai ihry must 

always be confined to matters belonging to the biography uf 

die observer; tliey can be such as *i see a canoid patch 
colour**;, but not such as *there is a dog*\ Jiiaiemenis of ihi?i 



latter kind always involve^ in their justification, some element 
of inference* 

In every assertion, two sides must be separated. On the 

subjective side, tlie assertion **expresses" a state of the speaker 
on the objective side, it intends to "indicate'' a "fact", and 
succeeds in this intention when true- The psychology of belief 
is concerned only with the subjective side^ the question of truth 

or falsehood also with the objective side. It is found that the 
analysis of what a sentence ^'expresses** renders possible a psycho- 
logical theory of the meaning of logical words, such as **or", 
**not", "all", and "some'\ 

in. Finally, there is the question of the relation between truth 
and knowledge* Attempts have been made to define **trudi" in 

terms of '^knowledge'', or of concepts, such as "verifiability 
which involve **knowledge*\ Such attempts, if carried out logi 
ally, lead to paradoxes which there is no reason to accept, 
conclude that **truth" is the fundamental concept, and that 
"knowledge'* must be <Jefined in terms of **truth", not vice versa. 

This entails the consequence that a proposition may be true 
although we can see no way of obtaining evidence either for 
or against it. It involves also a partial abandonment of the com 

plete metaphysical agnosticism that is favoured by the logical 


It appears from our analysis of knowledge that, unless it is 
much more restricted than we suppose* we shall have to admit 

principles of non-demonstrative inference which may be difficult 
to reconcile with pure empiricism- This problem emerges at 

various points, but I have refrained from 
because it would require for its treatment 
the present work, but mainly because any attempt at solution must 
be based upon an analysis of the matters considered in the fol- 
lowing chapters, and the disinteratedness of this analysis might 
be jeopardized by premature invatigatiion of its consequences. 



I h 

come now to a preliminary consideration of the question 


"what is a word?" But what I have to say now will be supple- 
mented by detailed discussions at later stages. 

Words, from the earliest times of which we have historical 
records, have been objects of superstitious awe. The man who 
knew his enemy's name could, by means of it, acquire magic 
powers over him. We still use such phrases as **in the name of 
the Law". It is easy to assent to the statement *'in the beginning 
was the Word". This view underlies the philosophies of Plato 
and Carnap and of most of the intermediate metaphysicians. 

Before we can understand language, we must strip it of its 
mystical and awe-inspiring attributes. To do this is the main 
purpose of the present chapter. 

Before considering the meaning of words, let us examine them 
first as occurrences in the sensible world. From this point of 
view, words are of four sorts: spoken, heard, written, and read. 
It will do no harm to assume a common-sense view of material 
objects, since we can always subsequently translate what has been 
said in common-sense terms into whatever pliilosophical lan- 

guage we may prefer. It is therefore possible to amalgamate 
written and read words, substituting for each a material object 

a mound of ink, as Neurath says — ^which is a written or printed 
word according to circumstances. The distinction between 
writing and reading is of course important, but almost everything 
that needs to be said about it can be said in connection with the 
difference between speaking and hearing. 

A given word, say "dog", may be uttered, heard, written, or 

read by many people on many occasions. What happens when 



a man says a word I shall call a "verbal utterance'*; what happens 
when a man hears a word I shall call a "verbal noise"; the physi- 

cal object which consists of a word written or printed I shall 
call a "verbal shape". It is of course obvious that verbal utter- 
ances, noises, and shapes are distinguished from other utterances, 
noises, and shapes, by psychological characteristics — ^by "inten- 
tion" or "meaning". But for the moment I wish, as far as may 
be, to leave these characteristics on one side, and consider only 
the status of words as part of the world of sense. 

The spoken word "dog" is not a single entity: it is a class 
of similar movements of the tongue, throat, and larynx. Just as 
jumping is one class of bodily movements, and walking another, 
so the uttered word "dog" is a third class of bodily movements. 
The word "dog" is a universal, just as dog is a universal. We 
say, loosely, that we can utter the same word "dog" on two 
occasions, but in fact we utter two examples of the same species, 
just as when we see two dogs we see two examples of the same 
species. There is thus no difference of logical status between 
dog and the word "dog": each is general, and exists only in 
instances. The word "dog" is a certain class of verbal utterances 
just as dog IS a certain class of quadrupeds. Exactly similar remarks 
apply to the heard word and to the written word. 

may be thought that I have unduly emphasized a very 
obvious fact in insisting that a word is a universal. But there 
is an almost irresistible tendency, whenever we are not on our 
guard, to think of a word as one thing, and to argue that, while 
there are many dogs, the one word "dog" is applicable to them 
all. Hence we come to think that dogs all have in common a 

certain canine essence, which is what the word "dog" really 
means. And hence we arrive at Plato and the dog laid up in 
heaven. Whereas what we really have is a number of more or 
less similar noises which are all ap 
or less similar quadrupeds. 

of more 


When we attempt to define the spo 
that we cannot do so without taking account of intention. Some 
people say "dawg", but we recognize that they mean "dog"* 



A German is apt to say "dok"; if we hear him say **De dok 
vaks hiss tail ven pleasst", we know that he has uttered an 
instance of the word "dog", though an Englishman who had 
made the same noise would have been uttering an instance of 
the word "dock". As regards the written word, similar con- 
siderations apply to people whose handwriting is bad. Thus 


while similarity to a standard noise or shape — ^that of a B3.C. 
announcer or copy-book calligraphist — ^is essential in defining 
an instance of a word, it is not sufficient, and the necessary 
degree of similarity to the standard cannot be precisely defined. 
The word, in fact, is a family,* just as dogs are a family, and 
there are doubtful intermediate cases, just as, in evolution, there 
must have been between dogs and wolves. 

In this respect print is preferable. Unless the ink is faded, it 
can hardly be doubtfiil, to a person of normal eyesight, whether 
the word "dog" is printed at a certain place or not. In fact, 
print is an artefact designed to satisfy our taste for classification. 
Two instances of the letter A are closely similar, and each very 

* >\ ' >i 


different from an instance of the letter B. By using black print 
on white paper, we make each letter stand out sharply against 
its background. Thus a printed page consists of a set of discrete 
and easily classified shapes, and is in consequence a lo^cian's 
paradise. But he must not delude himself into thinking that the 
world outside books is eaually charming. 

Words, spoken, heard, or written, diifer from other classes 
of bodily movements, noises, or shapes, by having "meaning". 
Many words only have meaning in a suitable verbal context 
such words as "than", "or", "however", cannot stand alone 

We cannot begin the explanation of meaning with such words 
since they presuppose other words. There are words, however ^ 
including all those that a child learns first— that can be used in 
isolation : proper names, class-names of familiar kinds of animals, 
names of colours, and so on. These are what I call "object-words" 


and they compose the "object-language", as to which I shall 

have much to say in a later chapter. These words have various 

* I owe diis way of putting the matter to Wittgenstein. 



peculiarities. First: their meaning is learnt (or can be learnt) 
confrontation with objects which are what they mean, or in- 
stances of what they mean. Second: they do not presuppose 
other words. Third: each of them, by itself, can express a whole 

proposition; you can exclaim "firel", but it would be pointless 


to exclaim "than!** It is obviously with such words that any 
explanation of "meaning" must begin; for "meaning**, like 
"truth** and "falsehood**, has a hierarchy of meanings, corre- 
sponding to the hierarchy of languages 

Words are used in many ways: in narrative, in request, in 
command, in imaginative fiction, and so on. But the most ele- 
mentary use of object-words is the demonstrative use, such as 
the exclamation "fox** when a fox is visible. Almost equally 
primitive is the vocative: the use of a proper name to indicate 
desire for the presence of the person named; but this is not 
(pdu so primitive, since the meaning of an object-word must be 
learnt in the presence of the object. (I am excluding such words 
as are learnt through verbal definitions, since they presuppose 
an ahready existing language.) 

It is obvious that knowing a language consists in using words 
appropriately, and acting appropriately when they are heard 
' is no more necessary to be able to say what a word 





tfian It IS for a cncketer to know the mathematical theory of 

impact and of projectiles. Indeed, in the case of many object 
words, It must be strictly impossible to say what they mean 

Z^i ^ ^,^"t° ogy for it is with them that language begins 

thing red. A child understands the heard word ««d" when ai 
assoaation has been estabUshed between the heard word and 
colour red; he has mastered the spoken word "red" when 
he notices something red, he is able to say "red" 
impulse to do so. 




say 'red** and has an 


The original learning of object-words isonethine-iheuse 

n Sr's'^rn;' ■^..'^ "-41'aLtr.;^ 

obvio4!'Ut^.^in*;f°'^ "^ ' "^ ^^ '^ 

imperative mood. When it 




seems to be a mere statement, it should be prefaced by the words 
"know that**. We know many things, and assert only some of 
them; those that we assert are those that we desire our hearers 
to know. "When we see a falling star and say simply "look!" 
we hope that this one word will cause the bystander to 
see it too. If you have an unwelcome visitor, you may kick 
him downstairs, or you may say '*get out!" Since the latter 

involves less muscular exertion, it is preferable if equally 

It follows that when, in adult life, you use a word, you do 
so, as a rule, not only because what the word **denotes'* is 
present to sense or imagination, but because you wish your 
hearer to do something about it. This is not the case with a 
child learning to speak, nor is it always the case in later years, 
because the use of words on interesting occasions becomes an 
automatic habit* If you were to see suddenly a friend whom you 

had falsely believed to be dead, you would probably utter his 
name even if neither he nor anyone else could hear you. But 
such situations are exceptional 
In the meaning of a sentence, there are three psychological 

elements: the environmental causes of uttering it, the effects of 
hearing it, and (as part of the causes of utterance) the 
which the speaker expects it to have on the hearer* 
We may say, generally, that speech consists, with some excep 

tions, of noises made by persons with a view to causing desired 
actions by other persons* Its indicative and assertive capacities, 

however, remain fundamental, since it is owing to them that, 
when we hear speech, it can cause us to act in a manner appro- 
priate to some feature of the environment which is perceived 

the speaker bat not by the hearer, or which the speaker 
remembers from past perceptions* In leading a visitor out of your 
house at night, you may say **here there are two steps down 


which causes him to act as if he saw the steps. This, however 
implies a certain degree of benevolence towards your visitor 

To state fact is by no means always the purpose of speech j it 

is just as possible to speak with a view to deceit, **Language was 



given us to enable us to conceal our thoughts." Thus when we 
think of language as a means of stating facts we are tacitly assum- 
ing certain desires in the speaker. It is interesting that language can 
state facts; it is also interesting that it can state falsehoods. When 
it states either/ it does so with a view to causing some action 
in the hearer ; if the hearer is a slave, a child, or a dog, the result 
is achieved more simply by using the imperative. There is, how- 
ever, a difference between the eifectiveness of a lie and that of 
the truth : a lie only produces the desired result so long as the 
truth is expected. In fact, no one could learn to speak unless 

truth were the rule: if, when your child sees a dog, you say 
cat'*, "horse**, or "crocodile**^ at random, you will not be able 

to deceive him by saying "dog" when it is not a dog. Lying 
is thus a derivative activity, which presupposes truth-spesiing 

as the usual rule. 

thus appears that, while most sentences are primarily im- 
perative, they cannot fulfil their function of causing action in 
the hearer except in virtue of the indicative character of object- 


words. Suppose I say "run!** and the person addressed con 
sequendy runs; this happens only because the word "run 
indicates a certain type of action. This situation is seen in its 
simplest form in military drill : a conditioned reflex is established, 
so that a certain kind of noise (the word of command) produces 
a certain kind of bodily movement. We may say, in this case, 
that the kind of noise in question is the name of the kind of 
movement in question. But words which are not names of bodily 
movements have a less direct connection with action. 

is only in certain cases that the "meaning" of a verbal 
utterance can be identified with the effect that it is intended to 
have on the hearer. The word of command and the word "look !" 
are such cases. But if I say "look, there*s a fox**, I not only seek 


to produce a certain action in the hearer, but I give him a motive 
for action by describing a feature of the environment In the 

of narrative speech, the distinction between "meaning" and 
mtcndwi effect is even more evident 

Only sentences have intended effects, whereas meaning is not 


WHAT IS A word: 


confined to sentences. Object-words have a meaning which does 
not depend upon their occurring in sentences. 

At the lowest level of speech, the distinction between sen- 
tences and single words does not exist. At this level, single words 
are used to indicate the sensible presence of what they designate. It 
is through this form of speech that object-words acquire their 
meaning, and in this form of speech each word is an assertion. 
Anything going beyond assertions as to what is sensibly present, 
and even some assertions which do not do so, can only be effected 
by means of sentences ; but if sentences contain object-words, what 
they assert depends upon the meaning of the object-words. There 
are sentences containing no object-words; they are those of logic 
and mathematics. But all empirical statements contain object- 
words, or dictionary words defined in terms of them. Thus the 
meaning of object-words is fundamental in the theory of empi- 
rical knowledge, since it is through them that language is con- 
nected with non-linguistic occurrences in the way that makes 
it capable of expressing empirical truth or falsehood. 



Chapter II 


5 -'**'*■'"-> 

I I 

Sentences may be interrogative, optative, exclamatory, or im- 
perative; they may also be indicative. Throughout most of the 
remainder of our discussions, we may confine ourselves to indi- 
cative sentences, since these alone are true or false. In addition 
to being true or false, indicative sentences have two other proper- 
ties which are of interest to us, and which they share with other 
sentences. The first of these is that they are composed of words, 
and have a meaning derivative from that of the words that they 
contain; the second is that they have a certain kind of unity, 
in virtue of which they are capable of properties not possessed 
by their constituent words. 

Each of these three properties needs investigation. Let us begin 
with the unity of a sentence. 

single grammatical sentence may not be. logically single. 
"I went out and found it was raining" is logically indistinguish- 
able from the two sentences: "I went out", "I found it was 

raining". But the sentence "when I went out I found it was 
raining" is logically single: it asserts that two occurrences were 
simultaneous. "Caesar and Pompey were great generals" is 
logically two sentences, but "Caesar and Pompey were alike in 
being great generals" is logically one. For our purposes, it will 
be convenient to exclude sentences which are not logically single, 
but consist of two assertions joined by "and" or "but" or 

"although" or some such conjunction. A single sentence, for our 
purposes, must be one which says something that cannot be said 
in two separate simpler sentences. 

Consider next such a sentence as "I should be sorry if you 
fell ill". This cannot be divided into, "I shall be sorry" and "you 



will fall ill"; it has the kind of unity that we are demanding of 
a sentence. But it has a complexity which some sentences do 
not have; neglecting tense, it states a relation between "I am 
sorry" and "you are ill". We may interpret it as asserting that 
at any time when the second of these sentences is true, the first 
is also true. Such sentences may be called "molecular" in relation 
to their constituent sentences, which, in the same relation, may 
be called "atomic". Whether any sentences are "atomic" in a 
non-relative sense, may, for the present, be left an open question; 
but whenever we find a sentence to be molecular, we shall do 
well, while we are considering what makes the unity of sen- 
tences, to transfer our attention, in the first place, to its 
atoms. Roughly, an atomic sentence is one containing only 
one verb; but this would only be accurate in a strictly logical 

This matter is by no means simple. Suppose I say first "A" 
and then "B"; you may judge: "the sound *A* preceded the 

sound *B' ". But this impUes "the sound *A' occurred" and "the 
sound *B' occurred", and adds that one occurrence was earlier 
than the other. Your statement, therefore, is really analogous to 


such a statement as "after I went out I got wet". It is a mole- 
cular statement whose atoms are "A occurred" and "B occurred". 
Now what do we mean by "A occurred"? We mean that there 
was a noise of a certain class, the class called "A". Thus 

when we say "A preceded B" our statement has a concealed 
logical form, which is the same as that of the statement: 
"first there was the bark of a dog, and then the neigh of a 

Let us pursue this a little further. I say "A". Then I say 
"what did I say?" Then you reply "you said *A' ". Now the 
noise you make when saying "A" in this reply is different from 
the noise I originally made ; therefore, if * * A* ' were the name 

of a particular noise, your statement would be false. It is only 
because "A" is the name of a class of noises that your statement 
is true; your statement classifies the noise I made, just as truly 
as if you had said "you barked like a dog". This shows how 



language forces us into generality even when we most wish to 
avoid it. If we want to speak about the particular noise that I 
made, we shall have to give it a proper name, say "Tom''; and 
the noise that you made when you said "A" we will call "Dick". 
Then we can say "Tom and Dick are A's". We can say "I said 
Tom" but not "I said Tom* ". Stricdy, we ought not to say 



said *A' "; we ought to say "I said an *A' ". AH this illus- 
trates a general principle, diat when we use a general term, such 
as "A" or "man", we are not having in our minds a universal 
but an instance to which the present instance is similar. When 
we say "I said *A* ", what we really mean is "I made a noise 
closely similar to the noise I am now about to make: *A* ". This, 
however, is a digression. 

We will revert to the supposition that I say first "A" and 

then "B". We will call the particular occurrence which was my 
first utterance "Tom", and that which was my second utterance 
"Harry". Then we can say "Tom preceded Harry". This was 
what we really meant to say when we said "the sound *A' pre- 
ceded the sound 'B' "; and now, at last, we seem to have reached 
an atomic sentence which does not merely classify. 

It might be objected that, when I say "Tom preceded Harry", 
this implies "Tom occurred" and "Harry occurred", just as when 
I said "the sound 'A' preceded the sound *B' ", that implied 
" 'A' occurred" and " *B' occurred". This, I think, would be a 
logical error. When I say that an unspecified member of a class 
occurred, my statement is significant provided I know what class 
is meant; but in the case of a true proper name, the name is 
meaningless unless it names something, and if it names some- 
thing, tihiat something must occur. This may seem reminiscent 
of the ontological argument, but it is really only part of the 
definition of "name". A proper name names something of which 
there are not a plurality of instances, and names it by a con- 
vention ad kocy not by a description composed of words with 
previously assigned meanings. Unless, therefore, the name names 
something, it is an empty noise, not a word. And when we say 
*Tom preceded Harry", where "Tom" and "Harry" are names 




of particular noises, we do not presuppose "Tom occurred** and 
Harry occurred", which are both strictly meaningless. 
In practice, proper names are not given to single brief occur- 
rences, because most of them are not sufficiently interesting 
When we have occasion to mention them, we do so by means 
of descriptions such as "the death of Caesar" or "the birth of 
Christ". To speak for the moment in terms of physics, we give 
proper names to certain continuous stretches of space-time, such 
as Socrates, France, or the moon. In former days, it would have 
been said that we give a proper name to a substance or collection 
of substances, but now we have to find a different phrase to 
express the object of a proper name. 

proper name, in practice, always embraces many occur- 
rences, but not as a class-name does: the separate occurrences 
are parts of what the name means, not instances of it. Consider 
say, "Caesar died". "Death" is a generic word for a number 
of occurrences having certain resemblances to each other, but 
not necessarily any spatio-temporal interconnection; each of 
diese is a death. "Caesar", on die contrary, stands for a series 
of occurrences, collectively, not severally. When we say "Caesar 
died", we say that one of the series of occurrences which was 
Caesar was a member of the class of deaths ; this occurrence is 
called "Caesar's death 

From a logical point of view, a proper name may be assigned 
to any continuous portion of space-time. (Macroscopic con- 
tinuity suffices.) Two parts of one man's life may have different 
names; for instance, Abram and Abraham, or Octevianus and 
Augustus. "The universe" may be regarded as a proper name 
for the whole of space-time. We can give a proper name to very 
small portions of space-time, provided they are large enough to 


be noticed. If I say "A" once at 6 p.m. on a given date, we can 
give a proper name to this noise, or, to be still more particular, 
to the auditory sensation that some one person present has in 
hearing me. But even when we have arrived at this degree of 
minuteness, we cannot say that we have named something desti- 
tute of structure. It may therefore be assumed, at least for the 




present, that every proper name is the name of a structure, not 
of sometliing destitute of parts. But this is an empirical fact, not 

a logical necessity. 

If we are to avoid entanglement in questions that are not 

linguistic, we must distinguish sentences, not by the complexity 

which they may happen to have, but by that implied in their 

Alexander preceded Caesar" is complex owing to the 



complexity of Alexander and Caesar; but "at preceded y 
not, by its form, imply that a: and y are complex. In fact, since 
Alexander died before Caesar was born, every constituent 
Alexander preceded every constituent of Caesar. We may thus 
accept '^x precedes y" as an atomic form of proposition, even 

if we cannot actually mention an x and a j which give an atomic 
proposition. We shall say, then, that z form of proposition is 
atomic if the fact that a proposition is of this form does not 
logically imply that it is a structure composed of subordinate 
propositions. And we shall add that it is not logically necessary 
that a proper name should name a structure which has parts. 

The above discussion is a necessary preliminary to the attempt 
to discover what constitutes the essential unity of a sentence; 
for this unity, whatever its nature may be, obviously exists in 
a sentence of atomic form, and should be first investigated in 
such sentences. 

In every significant sentence, some connection is essential 

between what the several words mean — omitting words which 
merely serve to indicate sjmtactical structure. 




"Caesar died" asserts the existence of a common member of two 
classes, the class of events which was Caesar and the class 

events which are deaths. This is only one of the relations that 
sentences can assert; syntax shows, in each case, what relation 

is asserted. Some cases are simpler than "Caesar died", others, 

are more complex. Suppose I point to a daffodil and say "this 
is yellow"; here "this" may be taken as the proper name of a 
part of my present visual field, and "yellow" may be taken as 
a class-name. This proposition, so interpreted, is simpler than 

Caesar died", since it classifies 

a given object; it is logically 



5 '^ **'***-'* 5 

analogous to "this is a death". We have to be able to know 
such propositions before we can know that two classes have a 

common member, which is what is asserted by "Caesar died*\ 
But "this is yellow** is not so simple as it looks. When a child 
learns the meaning of the word "yellow**, there is first an object 
(or rather a set of objects) which is yellow by definition, and 
then a perception that other objects are similar in colour. Thus 
when we say to a child "this is yellow*', what (with luck) we 
convey to him is: "this resembles in colour the object which is 
yellow by definition'*. Thus classificatory propositions, or such 
as assign predicates, would seem to be really propositions assert- 
ing similarity. If so, the simplest propositions are relational. 

There is, however, a diflference between relations that are sym- 
metrical and those that are asymmetrical. A relation is symmetrical 
when, if it holds between x and y, it also holds between y and x; 
it is asymmetrical if, when it holds between x and y, it cannot 
hold between y and x. Thus similarity is symmetrical, and so is 
dissimilarity; but "before**, "greater**, "to the right of", and so 
on, are asymmetrical. There are also relations which are neither 
symmetrical nor asymmetrical; "brother** is an example, since, 

X is the brother of j, y may be the sister of x. These and 
asymmetrical relations are called non-symmetrical. Non-sym- 
metrical relations are of the utmost importance, and many famous 
philosophies are refuted by their existence. 

Let us try to state what exactly are the linguistic facts about 
non-symmetrical relations. The two sentences "Brutus killed 
Caesar*' and "Caesar killed Brutus** consist of the same words, 
arranged, in each case, by the relation of temporal sequence. 
Nevertheless, one of them is true and the other false. The 
use of order for this purpose is, of course, not essential; Latin 

uses inflexions instead. But if you had been a Roman school- 
master teaching the difference between nominative and accusative, 
you would have been compelled, at some point, to bring in non- 
symmetrical relations, and you would have found it natural to 
explain them by means of spatial or temporal order. Consider 
for a moment what happened when Brutus killed Caesar: a dagger 



moved swiftly from Brutus into Caesar. The abstract scheme is 
"A moved from B to C", and the fact with which we are con- 

cerned IS that this is different from "A moved from C to B". 
There were two events, one A-being-at-B, the other A-being- 
at-C, which we will name x and y respectively. If A moved from 
B to Q a: preceded yi if A moved from C to B, j^ preceded x. 
Thus the ultimate source of the difference between "Brutus killed 
Caesar" and "Caesar killed Brutus" is the difference between 
*'x precedes ^" and ^y precedes x'\ where x and y are events. 
Similarly in the visual field there are the spatial relations above- 
and-below, right-and-left, which have the same property 
asymmetry. "Brighter", "louder", and comparatives generally, 
are ako asynmietrical. 

The unity of the sentence is peculiarly obvious in the case 
of asymmetrical relations: "a: precedes ^" and "y precedes x^ 
consist of the same words, arranged by the same relation 

temporal succession; there is nothing whatever in their ingredients 
to distinguish the one from the other. The sentences differ as 
wholes, but not in their parts ; it is this that I mean when I speak 
of a sentence as a unity. 

At this point, if confusions are to be avoided, it is important 
to remember that words are universals.* In the two sentential 
utterances *^x precedes y and ^'y precedes x*\ the two symbols 

<( 9> 

y are not identical, no more are the two symbols "y". Let 

1 and $2 be proper names of these two sentential utterances 


let Xx and Xj be proper names of the two utterances of "at 
1 and Ya of those of "y", and P^ and Pg of those of "precedes 
Then Si consists of the three utterances X, , P, , Y, in diat order 

It *lj *1 "* umtuiuci. 

and Sg consists of the three utterances Yg, Pg, Xg in that order 
The order in each case is a fact of history, as definite and un- 
alterable as the fact that Alexander preceded Caesar. When we 

observe that the order of words can be dianged, and that we 
can say "Caesar killed Brutus" just as easily as "Brutus killed 

* This does not imply that there are universals. It only asserts that the 
status of a word, as opposed to its instances, is the same as that of Dog as opposed 
to various particular 



Caesar", we are apt to think that the words are definite things 
which are capable of different arrangements. This is a mistake : 
the words are abstractions, and the verbal utterances can only 
have whichever order they do have. Though their life is short, 
they live and die, and they are incapable of resurrection. Every- 
thing has the arrangement it has, and is incapable of re-arrange- 



not wish to be thought needlessly pedantic, and I will 
therefore point out that clarity on this matter is necessary for the 
understanding of possibility » We say it is possiik to say either 
"Brums killed Caesar'* or "Caesar killed Brutus", and we do 
not realize that this is precisely analogous to the fact that it is 


possible for a man to be to the left of a woman on one occasion 
and for another man to be to the right of another woman on 

another occasion. For: let B be the class of verbal utterances 

which is the spoken word "Brutus"; let k be the class of verbal 
utterances which is the spoken word "killed"; and let y be the 

class of verbal utterances which is the spoken word "Caesar". 
Then to say that we can say either "Brums killed Caesar" or 
"Caesar killed Brutus" is to say that (i) there are occurrences 

X, P, 7, such that ;v is a member of jS, P is a member of #c, y is 
a member of y, x is just before P and P is just before y; (2) there 
are occurrences x\ P', y fulfilling the ^ove conditions as to 
membership of jS, if, y but such that y is just before P' and 

just before x\ I maintain that in all cases of possibility, there 
is a subject which is a variable, defined as satisfying some con- 
dition which many values of the variable satisfy, and that of 
these values some satisfy a fiirther condition while others do 
not; we then say it is "possible" that the subject may satisfy this 

fiirther condition^ Symbolically, if *'<l>x and ^jkt" and "^Jt: and 
not tpx" are each true for suitable values of Jtr, then, given tf>Xy tf/x 
is possible but not necessary. (One must distinguish empirical 
and logical necessity; but I do not wish to go into this question.) 
Another point is to be noted. When we say that the sentences 

"jfPy and "yP x" (where P is an asymmetrical relation) are 
incompatible, the symbols '^x" and "y" are universals, since, in 



I I I 


A I , 

I I 


our Statement, there are two instances of each; but they must 
be names of particulars. "Day precedes night" and **night pre- 
cedes day" are both true. There is thus, in such cases, an absence 
of logical homogeneity between the symbol and its meaning: 
the symbol is a universal while the meaning is particular. This 
kind of logical heterogeneity is very liable to lead to confusions. 
All symbols are of the same logical type: they are classes of 
similar utterances, or similar noises, or similar shapes, but their 
meanings may be of any type, or of ambiguous type, like the 
meaning of the word "type" itself. The relation of a symbol 
to its meaning necessarily varies according to the type of the 
meaning, and this fact is important in the theory of symbolism. 
Having now dealt with the possible confusions that may arise 
through saying that the same word can occur in two different 
sentences, we can henceforth freely use this expression, just as 
we can say "the giraffe is to be found in Africa and in the Zoo", 
without being misled into the belief that this is true of any 
particular giraffe. 

In a language like English, in which the order of the words 
is essential to the meaning of the sentence, we can put the matter 
of non-symmetrical relations as follows: given a set of words 
which is capable of forming a sentence, it often happens that it 
is capable of forming two or more sentences of which one is 
true while the others are false, these sentences differing as to 
the order of the words* Thus the meaning of a sentence, at any 
rate in some cases, is determined by the series of words, not by 
the c/iz^j. In such cases, the meaning of the sentence is not obtain- 
able as an aggregate of the meanings of the several words. When 
a person knows who Brutus was, who Caesar was, and what 
killing is, he still does not know who killed whom when he hears 
the sentence "Brutus killed Caesar"; to know this, he requires 
syntax as well as vocabulary, since the form of the sentence as 
a whole contributes to the meaning.* 

To avoid unnecessary lengthiness, let us assume, for the 
moment, that there is only spoken speech. Then all words have 

* Sometimes there is ambiguity: cf. ** the muse herself that Orpheus bore". 



a time order, and some words assert a time order. We know that^ 
if "x"" and ^y are names of particular events, tlien if **x pre 
cedes y' is a true sentence, **y precedes x" is a false sentence* 
My present problem is this; can we state anything equivalent 

but with events? It would seem that we are concerned with 
a characteristic of temporal relations, and yet, when we try to 
state what this characteristic is, we appear to be driven to stating 
a characteristic of sentences about temporal relations. And what 

to the above in terms which are not concerned with language 

applies to temporal relations applies equally to all other asym 
metrical relations. 

When I hear the sentence **Brutus killed Caesar*', I perceive 
the time-order of the words; if I did not, I could not know 

that I had heard that sentence and not **Caesar killed 

If I proceed to assert the time-order by the sentences 

H I 

preceded ^killed* '* and ** *killed* preceded *Caesar* **, I must again 
be aware of the time-order of the words in these sentences. We 
must, therefore, be aware of tlie time-order of events in cases 
in which we do not assert that they have that time-order^ for 

otherwise we should fali into an endless regress. What is it that 
we are aware of in such a case ? 

The following is a theory which might be suggested: when 

we hear the word **Brutus**, there is an experience analogous to 

that of the gradually fading tone of a bell; if the %vord was 
heard a moment aao. there is still now an akoiuthic sensation-. 

analogous to that of a moment ago, but fainter. Thus when we 

have just finished hearing the sentence **Brutus killed 

we are still having an auditory sensation which might be repre 
sented by 



whereas when we have just finished hearin 
Brutus", our sensation may be represented by 



These ar 


and it is this difference — so it may 


be contended — ^that enables us to recognize order in time. 
According to this theory, when we distinguish between "Brutus 
killed Caesar" and "Caesar killed Brutus", we are distinguishing, 
not between two wholes composed of exactly similar parts which 
are successive, but between two wholes composed of somewhat 
dissimilar parts which are simultaneous. Each of these wholes is 
characterized by its constituents, and does not need the further 
mention of an arrangement. 

In this theory there is, no doubt, an element of truth. It seems 
clear, as a matter of psychology, that there are occurrences, which 
may be classed as sensations, in which a present sound is com- 
bined with the fading ghost of a sound heard a moment ago. 
But if there were no more than this, we should not know that 

past events have occurred. Assuming that there are akoluthic 
sensations, how do we know their likeness to and difference from 
sensations in their first vigour ? If we only knew present occur- 
rences which are in fact related to past occurrences, we should 
never know of this relationship. Clearly we do sometimes, in 
some sense, know the past, not by inference from the present, 
but in the same direct way in which we know the present. For 
if this were not the case, nothing in the present could lead us 
to suppose that there was a past, or even to understand the 

Let us revert to the proposition : "if x precedes y, y does not 
precede xWi seems clear Aat we do not know this empirically, 
but it does not seem to be a proposition of logic* Yet I do not 
see how we can say that it is a linguistic convention. The pro- 
position ":\r precedes y* can be asserted on the basis of expe- 
rience. We are saying that, if this experience occurs, no experience 
will occur such as would lead to "y precedes x^\ It is obvious 
that, however we re-state the matter, there must always be a 
negation somewhere in our statement ; and I think it is also fairly 
obvious that negation brings us into the realm of language. 
When we say "y does not precede x'\ it might seem that we 

To decide this question, we need a discussion of proper names, to which 

we shall come later 



can only mean: "the sentence jy precedes x^ is false*'. For if we 
adopt any other interpretation, we shall have to admit that we 

can perceive negative facts, which seems preposterous, but per 

haps is not, for reasons to be given later. I think something 

similar may be said about "if" : where this word occurs, it must 
apply to a sentence. Thus it seems that the proposition we are 
investigating should be stated: "at least one of the sentences 
'x precedes y* and *y precedes jc' is false, if x and y are proper 
names of events". To carry the matter further demands a defini- 
tion of falsehood. We will therefore postpone this question until 
we have reached the discussion of truth and falsehood. 

Parts of speech, as they appear in grammar, have no very 
intimate relation to logical syntax. "Before" is a preposition and 
"precedes" is a verb, but they mean the same thing. The verb, 
which might seem essential to a sentence, may be absent in many 
languages, and even in English in such a phrase as "more haste. 

less speed". It is possible, however, to compose a logical kn 
guage with a logical syntax, and to find, when it has been con- 
structed, certain suggestions in ordinary language which lead up 

to it. 
The most complete part of logic is the theory of conjunctions. 

These, as they occur in logic, come only between whole sen- 
tences; they give rise to molecular sentences, of which the atoms 

are separated by the conjunctions. Tliis part of the subject is 
so fully worked out that we need waste no time on it. Moreover, 
all the earlier problems with which we are concerned arise in 
regard to sentences of atomic form. 
Let us consider a few sentences: (i) this is yellow; (2) this is 

before that; (3) A gives a book to B 

(i) In "this is yellow", the word "this" is a proper name. 
It is true that, on other occasions, other objects are called "this", 
but that is equally true of "John": when we say "here's John", 
we do not mean "here is some member of the class of people 
called *John* " ; we regard the name as belonging to only one 
person. Exactly the same is true of "this".* The word "men" 

* The word "this" will be discussed in the chapter on "Egocentric Particulars". 




is applicable to all the objects called severally **a man", but the 
word "these** is not applicable to all the objects severally called 
*'this" on different occasions. 

The word "yellow'* is more difficult. It seems to mean, as 
suggested above, "similar in colour to a certain object", this 
object being yellow by definition. Strictly, of course, since there 
are many shades of yellow, we need many objects which are 
yellow by definition : but one may ignore this complication. But 
since we can distinguish similarity in colour from similarity in 
other respects (e.g. shape), we do not avoid the necessity of a 
certain degree of abstraction in arriving at what is meant 
"yellow".* We cannot see colour without shape, or shape with 
out colour; but we can perceive the difference between the simi- 
larity of a yellow circle to a yellow triangle and the similarity 

of a yellow circle to a red circle. It would seem, therefore, that 
sensible predicates, such as "yellow", "red", "loud", "hard 

are derived from the perception of kinds of similarity. This 
applies also to very general predicates such as "visual", "audible", 
"tactile". Thus to come back to "this is yellow", the meaning 
seems to be "this has colour-similarity to that", where "this" 
and "that" are proper names, the object called "that" is yellow 
by definition, and colour-similarity is a dual relation which can 

be perceived. It will be observed that colour-similarity is a 
symmetrical relation. That is the reason which makes it possible 
to treat "yellow" as a predicate, and to ignore comparison. Per- 
haps, indeed, what has been said about the comparison applies 
only to the learning of the word "yellow"; it may be that, when 
learnt, it is truly a predicate.f 

(2) "This is before that" has already been discussed. Since 
the relation "before" is asymmetrical, we cannot regard the pro- 
position as assigning a common predicate to this and that. And 
if we regard it as assigning different predicates (e.g., dates) to 

* But consider Catnap's Lo^cher Aufbaw, yellow =» (by definition) a group 
all similar to this and each other, and not all similar to anything outside the 
group. This subject will be discussed in Chapter VL 

t This question has no substance. The object is to construct a minimum 
vocabulary, and in this respect it can be done in two ways, 





this and that, these predicates themselves will have to have an 
asymmetrical relation corresponding to "before". We may, for 
mally, treat the proposition as meaning "the date of this is earlier 
than the date of that'*, but "earlier" is an asymmetrical relation 
just as "before" was. It is not easy to find a logical method of 
manufacturing asymmetry out of symmetrical dara. 

The word "before", like the word "yellow", may be derived 
from comparison. We may start from some very emphatic case 
of sequence, such as a clock striking twelve, and, by taking other 
cases of sequence which have no other obvious resemblance to 
the striking clock, gradually lead to a concentration of attention 
on sequence. It seems clear, however — ^whatever may be the case 
in regard to "yellow" — that in regard to "before", this only 
applies to the learning of the word. The meaning of such words 
as "before" or "colour-similarity" cannot always be derived from 

comparison, since this would lead to an endless regress. Com 

parison is a necessary stimulus to abstraction, but abstraction 
must be possible, at least as regards similarity. And if possible 
in regard to similarity, it seems pointless to deny it elsewhere. 
To say that we understand the word "before" is to say that, 

when we perceive two events A and B in a time-sequence, we 
know whether to say "A is before B" or "B is before A", and 
concerning one of these we know that it describes what we 

(3) "A gives a book to B." This means: "there is an x such 

that A gives x to B and x is bookish" — ^using "bookish", for 
the moment, to mean the defining quality of books. Let us con- 
centrate on "A gives C to B", where A, B, C, are proper names. 
(The questions raised by "there is an x such that" we will con- 
sider presently.) I want to consider what sort of occurrence gives 
us evidence of the truth of this statement. If we are to know its 

* As to this, Dr. Sheffer has a way of distinguishing between the couple 
x-followed-by-y and the couple jz-followed-by-jc which shows that it is tech- 
nically possible to construct asymmetry out of symmetrical materials. But it 
can hardly be maintained that it is more than a technical device. 

Another way of dealing with asymmetry will be considered in a later 




truth, not by hearsay, but by the evidence of our own senses. 

we must see A and B, and see A holding C, moving C towards 

, and finally giving C into B's hands. (I am assuming that 
is some small object such as a book, not an estate or a copyright 
or anything else of which possession is a complicated legal 
abstraction.) This is logically analogous to "Brutus killed Caesar 
with a dagger". What is essential is that A, B, and C should all 
be sensibly present throughout a finite period of time, during 

which the spatial relations of C to A and B change. Schemati- 

cally, the geometrical minimum is as follows ; first we see three 
shapes Ai, B^, Q, of which Q is close to Ai ; then we see three 

very similar shapes Ag 




of which C2 is close to B3 . (I am 

omitting a number of niceties.) Neither of these two facts alone 
is sufiicient; it is their occurrence in quick succession that is 
asserted. Even this is not really sufiicient: we have to believe 

and Cg are respectively appearances 

that A, and A 



of the same material objects, however these may be defined. 



the fact that "giving** involves intention; but even 

so the complications are alarming. At first sight, it would seem 
that the minimum assertion involved must be something like 
this: "Aj, Bi, Q are appearances of three material objects at one 
time; Ag, Bg, Cg are appearances of the 'same' objects at a slightly 

later time; Q touches Aj but not Bj; C2 touches Bg but not Aj*'. 
I do not go into the evidence required to show that two appear- 
ances at different times are appearances of the "same*' object; 
this is ultimately a question for physics, but in practice and the 
law-courts grosser methods are tolerated. The important point, 
for us, is that we have apparently been led to an atomic form 
involving six terms, namely: "the proximity of Q to A^ and 
its comparative remoteness from R is an occurrence 


anterior to the proxim'.ty of Q to B2 and its comparative remote- 
ness from A2". We are tempted to conclude that we cannot avoid 
an atomic form of this degree of complexity if we are to have 
sensible evidence of such a matter as one person handing an 
object to another person. 

But perhaps this is a mistake. Consider the propositions: 



is near Ai, C is far from B,, At is simultaneous with Bi, B, is 

li J^i 

simultaneous with Q, Ai is slightly anterior to A2, Ag is simul- 
taneous with B2, Ba is simultaneous with Cg, Cg is near Bg, Cg 

is far from Ag . This set jof nine propositions is logically equivalent 
to the one proposition involving A^, Bi, Q, Ag, Bg, Cg. The one 
proposition, therefore, can be an inference, not a datum. There 
is still a difficulty: "near*' and "far" are relative terms; in astro- 
nomy, Venus is near the earth, but not from the point of view 
of a person handing something to another person. We can, how- 

ever, avoid this. We can substitute "Cx touches A^** for "Q is 

near Aj", and "something is between Q and Bj" for "Q is far 
from Bi". Here "touching*' and "between" are to be visual data. 
Thus the three-term relation "between" seems the most complex 

datum required. 

The importance of atomic forms and their contradictories is 
that — ^as we shall see — ^all propositions, or at least all non- 
psychological propositions justified by observation without in- 
ference are of these. forms. That is to say, if due care is taken, 
all the sentences which embody empirical physical data will assert 
or deny propositions of atomic form. All other physical sentences 
can theoretically be either proved or disproved (as the case may 
be), or rendered probable or improbable, by sentences of these 
forms ; and we ought not to include as a datum anything capable 
of logical proof or disproof by means of other data. But this is 
merely by way of anticipation. 

In a sentence of atomic form, expressed in a strictly logical 
language, there are a finite number of proper names (any finite 
number from one upwards), and there is one word which is not 
a proper name. Examples are: "jtr is yellow", "x is earlier thany", 
''x is between y and i*\ and so on. We can distinguish proper 
names from other words by the fact that a proper name can 
occur in every form of atomic sentence, whereas a word which 
is not a proper name can only occur in an atomic sentence which 
has the appropriate number of proper names. Thus "yellow 

demands one proper name, "earlier" demands two, and "between' 
demands three. Such terms are called predicates, dyadic relations 




triadic relations, etc- Sometimes, for the sake of uniformity, pre- 
dicates are called monadic relations. 

come now to the parts of speech, other than conjunctions 
that cannot occur in atomic forms. Such are "a**, "the", "aU*' 

"some'*, "many", "none". To these, I think, "not" should 
added; but this is analogous to conjunctions* Let us start with 

a". Suppose you say (truly) "I saw a man". It is obvious that 
"a man" is not the sort of thing one can see; it is a logical 
abstraction. What you saw was some particular shape, to which 
we will give the proper name A; and you judged "A is human 

The two sentences "I saw A" and "A is human" enable you to 
deduce "I saw a man", but this latter sentence does not imply 
that you saw A, or that A is human. When you tell me that you 

saw a man, I cannot tell whether you saw A or B or C or any 
other of the men that exist. What is known is the truth of some 
proposition of the form : 

"I saw X and x is human". 

This form is not atomic, being compounded of "I saw V and 



"je is human". It can be deduced from "I saw A and A is human 
thus it can be proved by empirical data, although it is not the 
sort of sentence that expresses a perceptual datum, since such 

a sentence would have to mention A or B or C or whoever it 

was that you saw. Per contra^ no perceptual data can disprove 
the sentence "I saw a man". 
Propositions containing "all" or "none" can be disproved 
by empirical data, but not proved except in logic and mathe- 
matics. We can prove "all primes except 2 are odd", because this 
follows from definitions; but we cannot prove **all men are 
.mortal", because we cannot prove th-^.t we have overlooked no 
one. In fact, "all men are mortal" is a statement about everything, 
not only about all men; it states, concerning every jc, that x is 
either mortal or not human. Until we have examined everything, 
we cannot be sure but that something unexamined is human but 
immortal. Since we cannot examine everything, we cannot knovf 
general propositions empirically, 



J « * *, * **-^5 

No proposition containing the (in the singular) can be strictly- 

proved by empirical evidence. We do not know that Scott was 
the author of Waverleyi what we know is that he was an author 
of Waverley. For aught we know, somebody in Mars may have 
also written Waverley. To prove that Scott was the author, we 
should have to survey the universe and find that everything in 
it either did not write Waverley or was Scott. This is beyond 
our powers. 

Empirical evidence can prove propositions containing **a'' or 
"some", and can disprove propositions containing "the**, "all'* 


or "none". It cannot disprove propositions containing "a" or 
"some", and cannot prove propositions containing "the", "all", 
or "none". If empirical evidence is to lead us to disbelieve pro- 
positions about "some" or to believe propositions about "all", 
it must be in virtue of some principle of inference other than 
strict deduction — ^unless, indeed, there should be propositions 
containing the word "all" among our basic propositions. 



Chapter III 


All persons who have learnt to speak can use sentences to describe 
events. The events are the evidence for the truth of the sentences. 
In some ways, the whole thing is so obvious that it is difficult to 
see any problem ; in other ways, it is so obscure that it is difficult 
to see any solution. If you say "it is raining**, you may know 
that what you say is true because you see the rain and feel it and 
hear it; this is so plain that nothing could be plainer. But difE- 
culties arise as soon as we try to analyse what happens when we 
make statements of this sort on the basis of imme(Uate experience. 
In what sense do we "know** an occurrence independendy of 
using words about it ? How can we compare it with our words, 
so as to know that our words are right? "What relation must 
subsist between the occurrence and our words in order that our 
words may be right? How do we know, in any given case, 


whether this relation subsists or not? Is it perhaps possible to 
know that our words are right without having any non-verbal ^ 

knowledge of the occurrence to which they apply ? 

Let us consider the last point first. It might happen that, on 
certain occasions, we utter certain words, and feel them to be 
right, without having any independent knowledge of the causes 

of our utterances. I think this does sometimes happen. You 
may, for instance, have been making strenuous effi>rts to like 

Mr, A., but . suddenly you find yourself exclaiming "I hate 
Mr. A.**, and you resJize that this is the truth. The same sort 
of thing, I imagine, happens when one is analysed by a psycho- 
analyst. But such cases are exceptional. In general, where present 
sensible facts are concerned at any rate, diere is some sense in 
which we can know Aem without using words. We may notice 





that we are hot or cold, or that there is thunder or lightning, and 
if we proceed to state in words what we have noticed, we merely 

register what we already know. I am not maintaining that this 

pre-verbal stage always exists, imless we mean, by "knowing' 
an experience, no more than that we have the experience ; but I 
do maintain that such pre-verbal knowledge is very common. It 
is necessary, however, to distinguish between experiences that 
we notice, and others that merely happen to us, though the 
distinction is only one of degree. Let us illustrate by some 

Suppose you are out walking on a wet day, and you see a 
puddle and avoid it. You are not likely to say to yourself: "there 
is a puddle; it will be advisable not to step into it**. But if some- 
body said "why did you suddenly step aside .^" you would 
answer "because I didn't wish to step into that puddle". You 
know, retrospectively, that you had a visual perception, to which 
you reacted appropriately ; and in the case supposed, you express 
this knowledge in words. But what would you have known, 
and in what sense, if your attention had not been called to the 
matter by your questioner ? 

When you were questioned, the incident was over, and you 
answered by memory. Can one remember what one never knew ? 
That depends upon the meaning of the word "know" 

The word "know" is highly ambiguous. In most senses of the 
word, "knowing" an event is a different occurrence from the 
event which is known; but there is a sense of "knowing" in 
which, when you have an experience, there is no diflFerence be- 
tween the experience and knowing that you have it. It might be 
maintained that we always know our present experiences; but 

this cannot be the case if the knowing is something different 
from the experience. For, if an experience is one thing and 
knowing it is another, the supposition that we always know an 
experience when it is happening involves an infinite multiplica- 
tion of every event. I feel hot; this is one event. I know that I 
feel hot; this is a second event. I know that I know that I feel 

hot; this is a third event. And so on ad infinitum^ which is absurd. 



We must therefore say either that my present experience is 
indistinguishable from my knowing it while it is present, or that, 
as a rule, we do not know our present experiences. On the whole, 
I prefer to use the word "know" in a sense which implies that the 
knowing is different from what is known, and to accept the 
consequence that, as a rule, we do not know our present experi- 

We are to say, then, that it is one thing to see a puddle, and 
another to know that I see a puddle. "Knowing'* may be defined 
as "acting appropriately"; this is the sense in which we say that 
a dog knows his name, or that a carrier pigeon knows the way 
home. In this sense, my knowing of the puddle consisted of my 
stepping aside- But this is vague, both because other things might 
have made me step aside, and because "appropriate" can only 

be defined in terms of my desires. I might have wished to get 

wet, because I had just insured my life for a large sum, and 
thought death from pneumonia would be convenient; in that 
case, my stepping aside would be evidence that I did not see the 
puddle. Moreover, if desire is excluded, appropriate reaction to 
certain stimuli is shown by scientific instruments, but no one 
would say that the thermometer "knows" when it is cold. 

What must be done with an experience in order that we may 
know it? Various things are possible. We may- use- w6rd» 
describing it, we may- remember it ^ithei? in .words or in images 
or we may merely "notice" it. But "noticing" is a matter of 
degree, and very hard to define; it seems to consist mainly in 
isolating from the sensible environment. You may, for instance 
in listening to a piece of music, deliberately notice only the part 
of the *cello. You hear the rest, as is said, "unconsciously" — ^but 
this is a word to which it would be hopeless to attempt to attach 
any definite meaning. In one sense, itymay be said that you 
"know" a present experience if it rouses in you any emotion 



however faint — if it pleases or displeases you, or interests or 

bores you, or surprises you or is just what you were expecting. 

There is an important sense in which you can know anything 

tliat is in your present sensible field. If somebody says to you 



I,* I - -fc J .1 1 f 

^■T*j-|jf i-l ^' ^rr ' ^ il ' ■■^^ 

I HI ^ r\ r I I 

•. if 

(«* _.t 



now seeing yellow?" or "do you hear a noise?" yoxi 




you were 

answer with perfect confidence, 

J, you were not noticing the yellow or the noise. And often 
can be sure that it was already there before your attention 
called to it. 

seems, then, that the most immediate knowing of which we 
2 experience involves sensible presence plus something more, 
that any very exact definition of the more that is needed is 
y to mislead by its very exactness, since the matter is essea- 
vague and one of degree. What is wanted may be called 
sntion" ; this is partly a sharpening of the appropriate sense- 
ans, partly an emotional reaction, A sudden loud noise is 
3st sure to command attention, but so does a very faint sound 
has emotional significance, 

very empirical proposition is based upon one or more sensible 
arrences that were noticed when they occurred, or immediately 
', while they still formed part of the specious present. Such 
arrences, we shall say, are "known" when they are noticed. 
. word "know" has many meanings, and this is only one of 
Ti; but for the purposes of our inquiry it is fundamental, 
rhis sense of "know" does not involve words. Our next 
Diem is : when we notice an occurrence, how can we formulate 
,ntence which (in a different sense) we "know" to be true in 
:ue of the occurrence ? 

f I notice (say) that I am hot, what is the relation of the 
irrence that I notice to the words "I am hot"? We may leave 
"I", which raises irrelevant problems, and suppose that I 

ely say 


there is hotness 



hotness", not 




ause I want a word for what can be felt, not for the physical 

.cept.) But as this phrase is awkward, I shall go on saying 
hot", with the above proviso as to what is meant, 
-et us be clear as to our present problem. We are no longer 
cerned with the question: "how can I know that I am hot?" 
s was our previous question, which we answered — however 
•atisfactorily — by merely saying that I notice it. Our question 
lot about knowing that I am hot, but about knowing, when 



■ tN^ 





n A 



if ■* 

-I --I 

:■■■- -'J 






n ^ 





P.BfHtf I. 


^'y ^j 


%i 'yi^^ ■ 

M ^ 

■:;.-l". ■' 

vi" ' 







M : ^ 




-'.■ ^ .^ " 






Sj( ■:■+■, ; 


akeady know this, that the words "I am hot'* express what 



■' I 








; * 




have noticed, and are true in virtue of what I have noticed. 

The words "express" and "true", which occur here, have no 

place in mere noticing, and introduce something radically new. 

Occurrences may be noticed or not noticed, but they cannot be 

noticed if they do not occur ; therefore, so far as mere noticing is 

concerned, truth and falsehood do not come in. I do not say Aat 

they come in only with words, for a memory which is in images 

may be false. But this may be ignored for the present, and in the 

case of a statement purporting to express what we are noticing, 

truth and falsehood first make their appearance with the use of 


When I am hot, the word "hot" is likely to come into my 

mind. This might seem to be the reason for saying "I am hot". 

But in that case what happens when I say (truly) "I am not 

hot"? Here the word "hot" has come into my mind although my 

situation is not of the kind that was supposed to have tliis effect. 

I think we may say that the stimulus to a proposition containing 

"not" is always partly verbal; some one says "are you hot,?" 

and you answer "I am not". Thus negative propositions will 

arise when you are stimulated by a word but not by what usually 

stimulates the word. You hear the word "hot" and you do not 

feel hot, so you say "no" or "I am not hot". In this case the word 

is stimulated partly by the word (or by some other word), partly 

by an experience, but not by the experience which is what the 
word means. 

The possible stimuli to the use of a word are many and various. 
You may use the word "hot" because you" are writing a poem in 
which the previous line ends with the word "pot". The word 
"hot" may be brought into your mind by the word "cold", or 
by the word "equator", or, as in the case of the previous dis- 
cussion, by the search for some very simple experience. The 
particular experience which is what the word "hot" means has 
some connection with the word over and above that of bringing 
the word to mind, since it shares this connection with many 
other things. Association is an essential part of the connection 





between being hot and the word "hot", but is not the 

The relation between an experience and a word differs from 


such other associations as have been just mentioned, in the first 
place, by the fact that one of the associated items is not a word. 
The association between "hot" and "cold", or between "hot" 

and **pot", is verbal. This is one important point, but I think 
there is another, suggested by the word "meaning". To mean 
is to intend, and in the use of words there is generally an intention, 
which is more or less social. When you say "I am hot", you 
give information, and as a r^le you intend to do so. When you 
give information, you enable your hearer to act with reference 
to a fact of which he is not directly aware ; that is to say, the 
sounds that he hears stimulate an action, on his part, which is 
appropriate to an experience that you are having but he is not. 
In the case of "I am hot", this aspect is not very noticeable, 
unless you are a visitor and your words cause your host to open 
the window although he is shivering with cold; but in such a 
case as "look out, there's a car coming", the dynamic effect on 
the hearer is what you intend. 

' An utterance which expresses a present sensible fact is thus, 
in some sense, a bridge between past and future. (I am thinking 
of such utterances as are made in daily life, not of such as philo- 
sophers invent.) The sensible fact has a certain effect upon A, 
who is aware of it : A wishes B to act in a manner which is ren- 

dered appropriate by this fact; therefore A utters words which 

'express" the fact, and which, he hopes, will cause B to act in a 
certain way. An utterance which truly expresses a present sensible 
fact enables the hearer to act (to some extent) as he would if the 
fact were sensible to him. 

The hearer who is relevant to the truth of a statement may be 
a hypothetical hearer, not necessarily an actual one. The state- 
ment may be made in solitude, or to a deaf man, or to a man 
who does not know the language used, but none of these circum 
stances affects its truth or falsehood. The hearer is assumed to 
be a person whose senses and linguistic habits resemble those of 



the speaker. We may say^, as a preliminary rather than a final 
definition, that a verbal utterance truly expresses a sensible fact 

when, if the speaker had heard the utterance without bein 
sensible of the fact, he would have acted as a result of the 
utterance as he did act as a result of the sensible fact. 

This is unpleasantly vague. How do we know how the man 
would have acted ? How do we know what part of his actual 
action is due to one feature of the environment and what to 
another.^ Moreover it is by no means wholly true that words 

produce the same effects as what they assert. "Queen Anne is 
dead" has very little dynamic power, but if we had been present 
at her deathbed the fact would probably have produced vigorous 
action. This example may, however, be ruled out, since we are 
concerned with the verbal expression of present facts, and his- 
torical truth may be left to be considered at a later stage. 

I think intention is only relevant in connection with sentences, 
not with words, except when they are used as sentences. Take 
a word like "hot", of which the meaning is sensible. It may be 
maintained that the only non-verbal stimulus to this word 

something hot. If, in the presence of something hot, the word 

"cold" comes into my mind, that will be because the word "hot" 

has come first, and has suggested the word "cold". It may be 

that every time I see a fire I think of the Caucasus, because of the 
lines : 

Can one hold a fire in his hand ' 
By thinking on the frosty Caucasus ? 

But the intermediate verbal association is essential and I shall 


not be led into the error of supposing that "Caucasus 

"fire". We may, then, say: if certain situations suggest a certain 

word without any verbal intermediary, the word means those 
situations, or something that they have in common. And in such 
a cffie the hearing of the word will suggest some situation of the 
kind m question. When I speak of a word ' 'suggesting' ' a situa- 
tion, I mean something not very definite, which may be an image 
or an action or an indpient action. 



A sentence, we shall say, differs from a word by having an 

intention, which may be only that of communicating information. 
But it is from the meanings of words that it derives its power of 
fulfilling an intention. For when a man utters a sentence, it is 
owing to the meanings of the words that it has power to influence 
the hearer's actions, which is what the speaker intends it to do. 
Sentences that describe experiences must contain words that 

have that kind of direct relation to sense that belongs to such 

a word as ''hoFTlteiong such words are the names of colours, 
the names of simple and familiar* shapes, loud, hard, soft, and 
so on. Practical convenience mainly determines what sensible 
qualities shall have names. In any given case, a number of words 
are applicable to what we experience. Suppose we see a red circle 
in a blue square. We may say "red inside blue" or "circle inside 
square". Each is an immediate verbal expression of an aspect 
of what we are seeing; each is completely verified by what we 

are seeing. If we are interested in colours we shall say the one, 
and if in geometry the other. The words that we use never exhaust 
all that we could say about a sensible experience. What we say is 
more abstract than what we see. And the experience that justifies 
our statement is only a fraction of what we are experiencing at 
the moment, except in cases of unusual concentration. As a rule 
we are aware of many shapes, noises, and bodily sensations in 
addition to the one that justifies our statement. 

Many statements based upon immediate experience are much 
more complex than "I am hot". This is illustrated by the above 
example of "circle inside square" or "red inside blue" or "red 
circle inside blue square". Such things can be asserted as direct 
expressions of what we see. Similarly we can say "this is hotter 
than that" or "this is louder than that", as the direct result of 
observation; and "this is before that" if both are within one 

specious present. Agai^ : if A is a circular patch of blue, B a 

circular patch of green, and C a circular patch of yellow, all 
within one visual field, we can say, as expressing what we see, 
"A is more like B than like C". There is, so far as I know 

, ^ . ^ ^..^^. no 

theoretical limit to the complexity of what can be perceived 




When I speak of the complexity of what can be perceived, the 
phrase is ambiguous. We may, for instance, observe a visual 
field, first as a whole, and then bit by bit, as would be natural 
in looking at a picture in a bad light We gradually discover that 
it contains four men, a woman, a baby, an ox, and an ass, as well 
as a stable. In a sense we saw all these things at first; certainly we 
can say, at the end, that the picture has these parts. But there may 
be no moment when we are analytically aware, in the way of 
sense-perception, of all these parts and their relations. When I 
speak of complexity in the datum, I mean more than what happens 

in such a caset I mean that we are noticing several interrelated 
things as several and as interrelated. The difference is most 
obvious in the case of music, where one may hear a total sound 
or be aware of the separate instruments and of the ingredients 
that make up the total effect. It is only in the latter case that I 
should speak of complexity in the auditory datum. The com- 
plexity that I am interested in is measured by the logical form of 
the judgment of perception; the simplest is a subject-predicate 
proposition, e.g. "this is warm"; the next is e.g. "this is to the 
left of that"; the next e.g. "this is between that and the other'*; 
aiid so on. Composers and painters probably go furthest in 
capacity for this kind of complexity. 

The important point is that such propositions, however 
complex they may become, are still direcdy based on experience, 
just as truly and completely as "I am warm". This is quite a 
different matter from Gestcdt as dealt with in Gestalt-psychology. 
Take (say) perception of the ten of clubs. Any person used to 
cards sees at once that it is the ten of clubs, and sees it by a per- 
ception of Gestalty not analytically. But he can also see that 
it consists of ten similar black patterns on a ^hite ground. This 
would be a remarkable feat, but in the case of the two or the three 

it would be easy. If, looking at the two of clubs, I say "this 
surface consists of two similar black patterns on a white ground", 
what I say is not merely an analysis of a visual datum, but is 
itself an expression of a visual datum ; that is to say, it is a propo- 
sition which I can know by die use of my eyes, without any need 




of inference. It is true that the proposition can be inferred from 
"this is a black pattern on a white ground", "so is that*' and "this 
is similar to that'*, but in fact it need not be so inferred. 

There is, however, an important distinction between propo- 
sitions which cannot be inferred and propositions which could 
be but are not. Sometimes it is very difficult to know to which 
class a proposition belongs. Take again the two of clubs, and the 
proposition "this is similar to that" applied to the two pippets 
We may give a iiame to the shape, and call it "clover-shaped", 
thus we can say "this is clover-shaped" and "that is dover- 
shaped"; also "this is black" and "that is black". We may infer 
"this and that are similar in shape and colour*** But this is, in 
some sense, an inference from the similarity of the two verbal 
utterances "clover-shaped** and the two verbal utterances 
. "black**. Thus a proposition of the form "this is similar to that'*, 
if not itself an expression of a sensible datum, must, it would 
seem, be derived from premisses of which at least one is of the 
same form. Suppose, for example, that you are conducting 
experiments in which it is important to record colour. You observe 
black, and speak the word "black" into your dictaphone. On a 
subsequent day you do the same thing again. You may then, on a 
third occasion, cause your dictaphone to repeat the two utterances 
"black**, which you observe to be similar. You infer that the 
colours you saw on two different days were similar* Here the 
dictaphone is inessential. If you see two black patches in quick 
succession, and say, in each case, "this is black**, you may, 
immediately afterwards, remember your words but have no 
visual memory of the patches ; in that case, you infer the similarity 
of the patches from that of the two utterances "black**. Thus' 
language affords no escape from similarity to identity. 

In such cases, the question as to what is inference and what is 
not is one that has, psychologically, no one definite answer 

In theory of knowledge, it is natural to attempt to reduce our 
empirical premisses to a minimum. If there are three propositions 
/7, y, r, all of which we assert on the basis of direct experience, 
and if r can be logically inferred from p and y , we shall dispense 





with r as a premiss in theory of knowledge^ In the above instance 

we see ** those are both black*'* But we can see •*ihis is black" 
and **that is black*' and infer **those are both black**. But tliis 

matter is not so simple as it looks. Logic deals^ not with verbal 

or sentential utterances^ but with propositions, or at least sen- 
tences. From the standpoint of logic^ when we know the two 
propositions ''this is black'* and **that is black'*, the word **black*' 

occurs in both. But as an empirical psychological fact, when we 

utter the two sentences, verbal utterances occur which are two 

different instances of the word **black*\ and in order to infer 



this and that are black" we need a further empirical premiss; 
the first utterance *black' and the second utterance *b!ack' are 

both instances of the word *biack**'* But in each case I can only 
utter an instance of the word, not the word itself, which remaim 
immovably in a Platonic heaven. 

Logic, and the whole conception of words and nentenca 
as opposed to verbal and sentential utterances^ is thus incurably 
Platonic. When I say **this is black" and **that is bbck**^ I want 
to say the same thing about both^ but I fail to do so; 1 only 

succeed when I say *'this and that are black**^ and then I say 

something different from either of the things I had previously 

said about this and about that* Thus the sort of generality that 

seems to be involved in the repeated use of the word **black" is 
an illusion; what we really have is similarity. To perceive the 

similarity of two utterances of the word **b!ack** is the same kind 
of thing as to perceive the similarity of two black patches. But 
in fact, when we use language;^ it is not necessary to penem 

similarity. One black patch causes one verbal utterance **black 
and another causes another; the patches are similar, and their 
verbal effects are similar, and the effects of the two verbal utter- 

ances are similar. These similariiies cm be observed* but need 

not be; all that is necessary is that they should in fact 
The importance of the question is in connection with logic and 
the theory of universak And it shows how complicated are the 
psychological presuppositions of the doctrine, which lode takes 

for granted, that the same word can occur on different occasions 




y 1 

erent sentential utterances and even in differt^nt sentences, 
f we are not careful, may be just as misleading as it would 
Infer that an okapi may be simultaneously in London and 
/ork, on the CT:>und that **an okapi is ru>\v in London" 


both true 

.n okapi is now in New York 

return from this excursion into logic, let us consider further 

happens w 

len we pas 



perception to an 

ic perception^ e,g» from **there is the two of clubs**, when 

there are two similar 

L* the parts of the 

rceive the whole shape as a unuy^ to 

marks on a white ground 


'e St! 

one kind of 

and their inter relations. Familiarity wi 
le material alTecis such analytic judgments. You are aware 

of cards contains thirteen clubs and four twos, and 


lave the 





twofold classification of cards 



'cr, Vvorks m 







ou to recognize a ten by 

'ittern^ whereas a person unfamiliar x's. 

mt up to ten 

'i^aH v^jV 

not in 


mieht have 

rder to see that the nattern is different 

a nine or an eight, but in order to give u its name 

is easy to exaggerate what is necessarv 

instance m 

ing. If you have to count a heap of nuts and you possess the 

lie risht order. 

habit of saving "oni% two, inrec 

in I 

an drop the nuis one by one intt) a bag, saying a number 

at ttie end vou will liave counted dnem without any 



memory or of apprehending numbers except as a stim 
mds ctmiing in a certain order as 

ites how much more words seem 



to kn 

habit. Th 
than is known 

e person who uses them* In like manner, a black object may 

you to say **t!ns is black** as a result of a mere mechanism 


Hit any re 

of the meaning o 

voiir words. Indeed 


is said in this thoughtless way is perhaps miirejikely to be 
:han what is said deliberately; fur if ymi know English tfiere 
iusal connection Ixnwcen a black i)bjeci asui the word **black'* 
:\ there is not between the same obiect and the name of a 

ent colour 

is wirni 


higli probability of 
to sentences stimulaied by the presence of tlie objects to 
'^ they refer. 




?. ) 






.f '*i 






J I 






i^ ■ 








V- ■* 

ir ^1- 








Kj ' 






■* . * 





.' k 
















































ifif r- 


V ■- 

^^z'*;. J.-M^ 






When you see a black object and say **this is black", you are 
not, as a rule, noticing that you say these words ; you know the 
thing is black, but you do not know that you say it is. I am using 
"know** in the sense of "notice", explained above- You can 




I ' 

notice yourself speaking, but you will only do so if, for some 
reason, your speaking interests you as much as the object does-- 


e.g., you are learning the language or practising elocution, 
you are — ^as we are — studying the relation of language to 
other facts, you will notice a connection between your words and 




c«T > 

the black object, which you nught express in the sentence: 
said 'this is black* because it is black**. This "because** demands 
close scrutiny. I have discussed this question in "The Limits of 

Empiricism*', Proceedings of the Aristotelian Society^ ^93S"^« 

At present I shall confine myself to a brief repetition of the rele- 
vant parts of that paper. 
We are concerned here with the relations of three propositions: 



u i> 


There is a black patch**, which we will call 

I said 'there is a black patch* ", which we will call "y" ; 

I said 'there is a black patch* because a black patch is there 




which we will call "r** 

In regard to r two questions arise: first, how do I know it? 
second, what is the meaning of the word "because** as it occun 


in this proposition : 

As to the first question, I do not see how to escape from the 
view that we know r, as we know p and y, because it is a sentence 
expressing an experiencf . But before we can adequately consider 
this view, we must be a little more definite about y , which may 
mean merely that I made certain noises, or may mean that I made 
an assertion* The latter says more than the former, since it states 
that the noises were made with a certain intention. I might have 
said "there is a black patch**, not because I wished to assert it, 
but because it is part of a poem. In that case, r would have been 
untrue. Therefore, if r is to be true, it is not sufficient that I should 



,*• , **, -W *^ V* «V, 

make the noises which constitute a sentential utterance of j, 
but I must make them with the intention of niaking an assertion 
about a present sensible fact. 




.e t 


jt this is somewhat too definite and explicit. "Intention" 
ests something conscious and deliberate, which ought not 
implied. Words may result from the environment just as 


tly as 

the sound "ow" 


am hurt. If some one asks 

y did you say 'ow'?*' and I reply "because I had a twinge 

DOthache* * 




because*' has the same meaning as in our 
position r: in each case it expresses an observed connection 
reen an experience and an utterance* We can use a word 
■ectly without observing this connection, but it is only 
irving the connection that we can explicitly know the meaning 
I word, providing the word is not one which has a verbal 
lition, but one which we learn by confrontation with what it 
ns. The difference between a cry of pain and the word "black" 
lat the former is an unconditioned reflex, which the latter is 


but this difference does not involve a difference in the word 

'. People who have learnt a certain language have 


uired an impulse to use certain words on certain occasions, 
this impulse, when it has been acquired, is strictly analogous 
jhe impulse to cry when hurt. 

J7e may have various reasons for uttering the sentence "there 
black patch". The fact may be so interesting that we exclaim 
:hout thought; we may wish to give information; we may wish 
attract someone's attention to what is happening; we may 
sh to deceive; we may, as in reciting poetry, be uttering the 
)rds without asserting anything. We can know, if we choose 
lich of these was our reason for uttering the words, and we 
ow this by observation — ^the kind of observation that is called 




In each case we have an observed connection 

tween two experiences. The simplest case is that in which the 
jht of the black patch is the reason for the exclamation "there 
a black patch !" This is the case contemplated in our proposition 

But the further discussion of the "because" 



the proposition r must be postponed until we have considered 
opositional attitudes. 




rl -r ■■:-S' 



I J 







<i .-I 



"jriff i 


Chapter IV 


Tarskij in his important book DiT fFaArkiitsBegriff m den fom^ 
alisierten Sprachm^ has shown that the words **true** and *1alse*\ 

as applied to the sentences of a given language^ always require 
another language, of higher order^ for tlneir adequate definitm 
The conception of a hierarchy of languages is involved in the 

theory of types^, which, in some form, is necessary for the solution 
of the paradoxes; it plays an important part in Carnap's work as 

well as in Tarski's. I suggested it in my introduction to Wittgen 

stein's Tractatus^ as an escape from his theory thai syntax can 

only be "shown", not expressed in words* The arguments for 

the necessity of a hierarchy of languages are overwhelming, 

and I shall henceforth assume their validity 



These arguments are derived from the paradoxesj their applicatbitity to die 

words **tfue" and "false** is derived from ihe paradoK af t\m liar. 
My inference from the paradox of the iiar was, in outline* m follows^; A man 
says *'I am lying**, i.e. "there is a proposition p such that I M'mn p and p h false**, 

We may> if we likej make the matter more precise by supposing that, n 5.J0, 
says "between 5*25^ and 5,31 I make a false statement**, foul fhai ihroughoat the 

of the two minutes concerned he says nociiing* Let us call this statemt^nt 
q^\ liq is mie> he makes a false statement during the crucial two minuinj but 

« »» 

q is his only statement in this periods therefore q must be false. Bui if ^ k false, 
then every stetement that he makes daring the two minutes mmi be true, and 
therefore q must be true, since he makes it during the two minutet • Thus if q is 
true it is false, and if it is false it is true. 

Let **ACpy' mean **I assert j» between $.z^ and 5*1 1**. Tbm q is **ihere is % 
proposition jp such that k{p) mdp is false*'. The contradiction emei^es from the 
supposition that q is tlie proposition p In question* But if tljere k a hierarchy of 
meanings of the word **false'* corresponding to a hierarchy of proposiiloRH, we 

shall have to substitute for ^ something more definite, i»e. ''there is a proposition 
p of order n, such that A(p) and p has falsehood of order b'\ Here n may be any 

integer: but whatever integer it is, q will be of order n + h a«d will not be capable 
of truth or falsehood of order n. Since I make no assertion of order «, q is fals*?i 



1\ ml 


\ ' ^ 




1* T'S-BP^I 

* .f 


> J* 



hierarchy must extend upwards indefinitely 




since, if it did, language could never 
therefore, be a language of lowest type 

, but not 

et started 

ne such language, not the only possible one 

shall call 







sometimes the 






My purpose, in the present chapter, is to define and 

this basic langua 

The languages which follow in the 

shall call secondary, tertiary, and so on; it is to be 

ood that each language contains all its predecessors 
primary language 

we shall find, can be 



attempting formal 

^ and psychologically 

Dns it will be well to make a preliminary informal explora 

clear, from Tarski's argument 


that the words 



cannot occur in the primary 




for these 

as applied to sentences in the n^^ language, belong to the 
'^ language. This does not mean that sentences in " 


y language are neither true nor false, but that 


f( »» 



in this language 


the two 

IS true 


is a 


belong to tlie secondary langua 

risis is, indeed 


s apart from Tarski*s argument* For, if there is a primary 

ge, its words must not be such as presuppose the existence 
ngua^e. Now "true*' and *'false** are words applicable to 

es, and thus presuppose the 
mean to deny that 

of language 

a memory consisting of images, not 


be **true** or ** 



is is in a somewhat 

It sense 


which need not concern us at present.) In the 
therefore, tliough we can make assertions, we 

those of others are either 

y langua 

: say that our own assertions or 




n I say that we make assertions in the primary language^ 
guard against a misunderstanding, for the word "assertion" 

,. q is not a pomlhk value of p, the argument that q is ako true collap^s. 
1 who says '*! am telling a Ik of order «*' is tdling a Ue, but of order 
Other ways of evading ilic paradox have been suggested, c*g. by Ramsey 

of Mathematics 

p* 4^ 

hierarchy of languages is not identical with Curnap's or larsk* 






pL^^OW ^ 


I ^' 

.l-tl ^1 






\ ' 











s. ^'"1 



vJ^n •• 


^-S ; 


V ^ '"Sj^Jiri^'r 

-li \'<* 







JS 'k^ 

Kii .'J 




^'JH I* 

I ' 












1^1^ hU 'Vi 


--i . 


is ambiguous. It is used, sometimes, as the antithesis of denial 
and in this sense it cannot occur in the primary language, Denia 
presupposes a form of words, and proceeds to state that this forn 
of words is false. The word "not" is only significant when attachet 
to a sentence, and therefore presupposes language. Consequently 

if "/' is a sentence of the primary language, * not-/ is a sentenci 
of the secondary language. It is easy to fall into confusion, sina 
"/ *, without verbal alteration, may express a sentence only pos* 
sible in the secondary language. Suppose, for example, you havt 
taken salt by mistake instead of sugar, and you exclaim "this is 
not sugar"* This is a denial, and belongs to the secondary language 
You now use a different sprinkler, and say with relief "this « 
sugar". Psychologically, you are answering affirmatively 
question **is this sugar .^" You are in fact saying, as unpedantic- 
ally as you can: "the sentence *this is sugar' is true"* Therefore 
what you mean is something which cannot be said in the primary 
language, although the same form of words can express a sentence 

in the primary 

assertion which is the antithesis 
of denial belongs to the secondary language j the assertion which 
belongs to the primary language has no 

Just the same kind of considerations as apply to **not" apply 
to "or'* and "but" and conjunctions generally. ConjunctionSj 
as their name implies, join other words, and have no nieaning in 
isolation; they therefore presuppose the existence of a language. 
The same applies to "all" and "some" ; you can only have all 
of something, or some of something, and in the absence of other 
words "all" and "some" are meaningless. This arguments also 
applies to "the". 

Thus logical words, without exception, are absent from 
primary language. All of them, in fact, presuppose propositional 
forms: "not" and conjunctions presuppose propositions, while 
"all" and "some" and "the" presuppose propositional functions. 

Ordinary language contains a number of purely syntactical 
words, such as "is" and "than", which must obviously 
excluded from the primary language. Such words, unlike those 
that we have hitherto considered, are in fact wholly unnecessary. 


H^,i-.Hrfiu^iirfii'tt^''.'' 1^ ^^T.-'rrr*'?.'" \^i^i-'''j.'\\fv, . . 'sf ■'' 

^ ^ 

h ** r 

I' ■■ 



"- 'I'*'. 1 OH ^^ 






o not appear in symbolic logical languages. Instead 

earlier than 


/' a 

logical language 

A precedes 

instead of "A 

"yellow (A)"; instead 

are smiling villains' ^ we say : it is false 

all values of 

;r X does not smile or x is not a villain" are false, "Existence** 







traditional metaphysics 


tatized forms of certain meanings of "is". Since "is" does 
elong to the primary language 

"existence" and 

are to mean anything, must be linguistic concepts not 
ly applicable to objects. 

.ere is another very important class of words that must be 
St provisionally^exduded^amely such words as "believe" 


:e , "doubt", all of which, when they occur in a sentence 

be followed by a subordinate sentence telling what 

s believed or desired or doubted. Such words 
Deen able to discover, are always psychological, and involve 
call "propositional attitudes". For the present 

point out diat they differ from such words as "or" in 
iportant respect, namely that they are necessary 
■ption of observable phenomena. If I want to see the paper 
.s a fact which I can easily observe, and yet "want" is a 

a subordinate sentence 

which has to be followed 

ing significant is to result. Such words raise problems 
xe perhaps capable of being analysed in such a way 
them able to take their place in the primary language. 
;s is not pnma fade possible, I shall for the present assume 
:hey are to be excluded- I shall devote a later chapter to the 
ssion of this subject. 

2 can now partially define the primary or object-language as 
^uage consisting wholly of "object-words",* where "object- 

, as words having meaning in 

s" are 

defined, logically 



and, psychologically, as words which have been 


■ without its being necessary to have previously learnt any 
■words. These two definitions are not strictly equivalent, 

^here must be syntax:, but it need not be rendered explicit by the use of 
rtical words, such as **is". 

1 1 














Ci's iiT'i. 





and where they conflict the logical definition is to be preferred 

They would become equivalent if we were allowed to suppose 
an indefinite extension of our perceptive faculties. We could not, 
in fact, recognize a chiliagon by merely looking at it, but \ve 
can easily imagine beings capable of this feat. On the other hand, 
it is clearly impossible that any being's knowledge of language 

should begin with an understanding of the word 




the meaning of this word is not learnt from a formal definition, 
Thus in addition to the class of actual object-words, there is a 
class of possible object-words. For many purposes the class of 
actual and possible object-words is more important than 
class of actual object-words* 

In later life, when we learn the meaning of a new word, we 
usually do so through the dictionary > that is to say, by a definition 
in terms of words of which we already know the meaning. But 
since the dictionary defines words by means of other words 
there must be some words of which we know the meaning without 
a verbal definition. Of these words, a certain small number do 



not belong to the primary language; such are the words 
and "not". But the immense majority are words in the primary 
language, and we have now to consider the process of learning 
what these words mean. Dictionary words may be ignored, since 

they are theoretically superfluous ; for wherever they occur they 

can be replaced by their definitions. 

In the learning of an object-word, there are four tilings to be 
considered : the understanding of the heard word in the presence 
of the object, the understanding of it in the absence of the object^ 
the speaking of the word in the presence of the object, and the 
speaking of it in the absence of the object. Roughly speakinff. this 

1 1 


is the order in which a child acquires these four capacities 
Understanding a heard word may be defined behaviourisu- 

rally or in terms of individual psychology. When we say that a 
dog understands a word, all that we have a right to mean is that 

he behaves in an appropriate manner when he hears it; what he 

for example, the process 



we cannot know. Conside 

ot teaching a dog to know his name. The process consists 


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ailing him, rewarding him when he comes, and punishing him 

/hen he does not. We may imagine that, to 

the dog, his name 

leans: "either I shall be rewarded because I approach my master 


shall be punished because 


Which alternative is 

onsidered the more probable is shown by the tail. The associa- 
on, in this case, is a pleasure-pain association, and therefore 

nperatives are what the 

understands most easily. 

:an understand a sentence in the indicative, provided its content 

as sufficient emotional importance; 


^dinner !" which means, and is understood to mean : 

sen tence 

u are 

ow about to receive the nourishment that you desire". When I 
ay that this is understood, I mean that, when the dog hears the 

/ord, he behaves very much as he would if you 

plate of 

bod in your hand. We say the dog "knows'* the word, but what 
7e ought to say is that the word produces behaviour similar 
lat which the sight or smell of a dinner out of reach would 

The meaning of an object- word can only be learnt by hearing 
: frequently pronounced in the presence of tlie object. The asso- 
:iation between word and object is just like any other habitual 
.ssociation, e.g. that between sight and touch. When the associa- 
ion has been established, the object suggests the word, and the 
7ord suggests the object, just as an object seen suggests sensations 
)f touch, and an object touched in the dark suggests sensations 
ight. Association and habit are not specially connected with 
anguagej they are characteristics of psychology and physiology 
■enerally. How they are to be interpreted is, of course, a difficult 
.nd controversial question, but it Is not a question which specially 
oncerns the theory of language 

As soon as the association between an object-word and what 

^'understood'* in the 

means has been established, the word is 

bsence of the object, that is to say, it **suggests** tlic object in 

;xactly the same sense in which sight and touch 




Suppose you are with a man who suddenly says * 

sees a fox, and suppose that,, though you hear him, you do not 


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see the fox. What actually happens to you as a result of your 
understanding the word "fox"? You look about you, but this 
you would have done if he had said "wolP' or "zebra". You may 
have an image of a fox. But what, from the observer's standpoint, 
shows your understanding of the word, is that you behave 
(within limits) as you would have done if you had seen the fox. 
Generally, when you hear an object-word which you under- 
stand, your behaviour is, up to a point, that which the object 
itself would have caused. This may occur without any "mental" 
intermediary, by the ordinary rules of conditioned reflexes, 

since the word has become associated with the object 
morning you may be told "breakfast is ready", or you may 
smell the bacon. Either may have the same effect upon your 
actions. The association between the smell and the bacon is 
"natural", that is to say it is not a result of any human behaviour* 
But the association between the word "breakfast" and breakfast 
is a social matter, which exists only for English-speaking people. 
This, however, is only relevant when we are thinking of the 
community as a whole. Each child learns the language of its 
parents as it learns to walk. Certain associations between words 
and things are produced in it by daily experience, and have as 
much the appearance of natural laws as have the properties of 
eggs or matches; indeed they are exactly on the same level so 
long as the child is not taken to a foreign country. 

is only some words that are learnt in this way. No one 
learns the word "procrastination" by hearing it frequently pro- 
nounced on occasions when some one is dilatory. We learn, 
by direct association with what the word means, not only proper 
names of the people we know, class-names such as "man" and 
"dog", names of sensible qualities such as "yellow", "hard". 

sweet", and names of actions such as "walk"^ "run"^ "eat 

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"drink", but also such words as "up'' and "down", "in" and 
"out", "before" and "after", and even "quick" and "slow". 
But we do not learn in this way either complicated words such as. 
"dodecahedroji" or logical words such as "not", "or", "the", 




"all", "some". Logical words, as we have seen, presuppose 




iguage; in fact, they presuppose what, in an earlier 



Spoke of as "atomic forms". Such words belong to a stage of 
iguage that is no longer primitive, and should be carefully 
.eluded from a consideration of those ways of speaking which 
2 most intimately related to non-linguistic occurrences. 
What kind of simplicity makes the understanding of a word 
to an example of understanding aii object-language? For it is 

be observed that a sentence may be spoken in the object- 

iguage and understood in a language of higher order 

jsa. If you excite a dog by saying "rats!" when there are no 

ts, your speech belongs to a language of higher order, since it 

not caused by rats, but the dog's understanding of it belong 




the object-language. A heard word belongs to the object- 
.nguage when it causes a reaction appropriate to what the word 
.eans. If some one says "hark, hark, the lark", you may listen, 

you may say 


at heaven 

gate smgs 



in the former case 


'hat you have heard belongs to the object-language, in the latter 
ase, not. Whenever you doubt or reject what you are told, your 





earing does not belong to the object-language; 
ase you are lingering on the words, whereas in the object- 
nguage the words are transparent, i.e. their effects upon your 
ehaviour depend only upon what they mean, and are, up to a 
oint, identical with the effects that would result from the sensible 
resence of what they designate. 

In learning to speak, there are two elements, first, the muscular 
exterity, and second, the habit of using a word on appropriate 

casions* We may ignore the muscular dexterity, which can be 
-cquired by parrots. Children make m.any articulate sounds 
pontaneously, and have also an impulse to imitate the sounds 
lade by adults. When they make a sound which the adults 
:onsider appropriate to the environment, they find the results 
Dleasant Thus, by the usual pleasure-pain mechanism which is 
mploy ed in training performing animals, children learn, in time, 
:o utter noises appropriate to objects that are sensibly present, 
nd then, almost immediately, they learn to use the same noises 
ivhen they desire the objects. As soon as this has happened, they 













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possess an object-language: objects suggest their names, theii 
names suggest them, and their names may be suggested, not 
only by the presence of the objects, but by the thought of them. 

pass now from the learning of an object-language to its 
characteristics when learnt. 

We may, as we have seen, divide words into three classes: 
(i) object-words, of which we learn the meaning by directly 
acquiring an association between the word and the thing; (2) 
propositional words, which do not belong to the object-language; 
(3) dictionary words, of , which we learn the meaning through a 
verbal • definition. The distinction between (i) and (3) varies 
considerably from one person to another. "Pentagram** is to 
most people a dictionary word, but to a child brought up in a 
house decorated with pentagrams it might be an object-word, 
"Swastika" used to be a dictionary word, but is so no longer. It 
is important to note, however, that there must be object-words 
since other^dse dictionary definitions could not convey anything, 

Let us now consider how much, in the way of language, can 
be done by object-words alone. I shall assume, for this purpose 
that the person considered has had every possible opportunity 
of acquiring object-words; he has seen Mount Everest and 
Popacatapetl, the anaconda, and the axolotl, he is acquainted with 
Chiang Kai-shek and Stalin, he has tasted birds' nests and shark*s 
fins, and altogether has a wide experience of the sensible world. 
But he has been too busy seeing the world to acquire the use of 
such words as "not", "or* V "some", etc. If you say to him "is 
there any country that you have not visited ?" he will not know 
what you mean. The question is : what will such a person know 
and what will he not know ? 

Can we say: "he will know everything that can be known by 
observation alone, but nodiing that needs inference"? Let us 
first alter our question, and ask, not what can he know, but what 
can he express in words? 




To begin with: if he can put every observable fact into 
words, he must have as many words as facts ; now some words 
are among facts ; therefore the number of his words must 




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nite. This is impossible; consequently there are facts he 
/es unexpressed. The case is analogous to Royce's bottle with 
abel on which there was a picture of the bottle, including, of 
arse, a picture of the label* 

3ut although he must leave out some observable facts, there 
lot any one observable fact of which we can say "he must 

ve this one out." He is in the position of a man who wishes 

pack three suits into a suit-case that will only hold two; he 

ist leave one out, but there is not one that he must leave out. 

our travelled friend, we will suppose, sees a man called Tom 


without difficulty he says 


see Tom**. This remark is 

elf an observable fact, so 



sav that I see Tom 


lis again is an observable fact, so 




say that 


at I see Tom". There is no one definite point at which he must 

•eak off this series, but he must break it off somewhere, and at 

at point there is an observable fact which he does not express 

words. It seems, therefore, that it is impossible for a mortal 

give verbal expression to every observable fact, but that 

vertheless, every observable fact is such that a mortal could 

ve verbal expression to it. This is not a contradiction. 

We have thus two different totals to consider: first, the total 

" the man's actual statements, and secondly the total of possible 

:atements out of which his actual statements must be chosen. 

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ut what is a "possible" statement.^ Statements are physical 

, like thunderstorms or railway accidents; but at 

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;ast a novelist or poet can describe a thunderstorm that never 
Dok place. But it is difficult to describe a statement without 
laking it. In describing a political speech, you may remark: 

and then 

dUows a statement ; that is to say, in order to say that a statement 
/as not made, we have to make 

what Sir Somebody So-and-So did not say was 


It, except 

in the rare instances 
>f statements that have names, such as the Coronation Oath. 

There are, however, ways of avoiding this difficulty, the best 
Df which is due to Godel. "We assume a completely formalized 
anguage, with an entirely explicit vocabulary and syntax. We 
assign numbers to the words of the vocabulary, and hence, 

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arithmetical rules, to ail possible sentences in the language. 

If, as we are assuming;, the initial vocabulary is finite, but theie 

IS no limit to the length of sentences (except that they must k 
finite), the number of possible sentences will be the same as the 
number of finite integers. Consequently^ if n is any finite integer, 
there is one 

which is the «'^, and our rules 
will enable us to construct it, given n. We can now make al 

sorts of statements about hit. A's statements, without having 
actually to make his statements* We might say *'Mn A never 
makes a statement of which the number is divisible by ij**, or 
"all Mr- A's statements have numbers which are prime*' 
But there are still diftkulties, of the kind emphasized by the 

finitists. We are used to thinking of the wliole series of natural 
numbers as in some sense **given*', and %ve have utilized this 

idea to give definiteness to the theory of possible statements. 

But how about numbers which no one lias ever mentioned or 
thought of? What is a number except something that occurs in a 
statement? And, if so, a number that has never been mentioned 

, •* -^^j 

involves a possible statement, which cannot, witlioul circularity, 
be defined by means of such a number. 
This subject cannot be pursued at present, since it would take 

us too deep into the subject of logical language. Let us see 
whether, ignoring such logical points, we can be a little moi« 
definite about the possibilities of a language which contains 
only object-words. 

Among object-words, as we saw, are included a certain number 
of verbs, such as **run**, ^*eat**, **shout*', and even some prepo- 

sitions such as **in'' and **above** and **before**. All that is esi^fntiai 
to an object-word is some similarity among a set of phenomena, 

which is sufficiently striking for an association to be established 
between instances of the set and instances of the word for the 

set. the method of establishines the association beinE that* for some 


time, the word is frequently heard when a member of the set is 
seen. It is obvious that what can be learnt in this way depends 
upon psychological capacity and interest. The similarity berweai 
different instances of eating is likely to strike a child, because eating 


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iteresting; but in order to learn in this way the meaning of the 

"dodecagon" a child would need a precocity of geometrical 


.rest surpassing Fascai's and a superhuman capacity for per- 
ring Gestalt. Such gifts are^ fiowever^ not logically impossible 
. how about "or"? Yoa cannot show a child examples of it 
:he sensible world. You can say: **wiU you have padding or 

but if the child says yes, you cannot find a nutriment 



'ch is "pudding-or-pie*\ And yet "or'* has a relation to experi- 
:e; it is related to the experience of choice. But in choice we 
/e before us two possible courses of action^ that is to say, two 
aal thoughts as to courses of action. These thoughts may not 

'olve explicit sentences^ but no change is made in what is 

'^' '' " as an 

ntial if we supposed them to be explicit. Thus '*or'' 


nent of experience^ presupposes sentences, m something 
intal related in a similar manner to some other fact* When we 




this or that** we are not saying something directly applicable 
an object, but are stating a relation between saying **this* 
\ saying **that'\ Our statement is about statements, and only 
directly about objects* 

Let us consider, in like manner, negative propositions which 
*m to have an immediate relation to experience* Suppose you 




there is butter in the krcJer, bur no cheese*\ Ahhoii 


y seem equally based upon 




there is butter 


experience in the larder 




not cheese 



e really on a very different level There was a definite occurrence 
lich was seeing butter, and which might have put the word 



into your mind even if you had not been thinkin 

itter- But there was no occurrence which could be described as 

aot seeing cheese** or as ** 

the absence of cheese 

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ust have looked at everytlung in the larder, and judged^ in each 


, **this is not cheese*'- You judged this, you did not jt*e it 
Du saw what each thing was^ not what it was not* To jud 


this is not cheese'*, you must have the word 


c heese 



or some 


in your mind already* There is a clash between what 

* This subject will be discussed again in a taur chapter* jind what h m%4 stovt 
ill be at once am|>lifii<?d md gmrdi^d ap;aimt a toci litfral in«t*rpr«tica«ion. 




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you see and the associations of the word 





and so 




this is not cheese*\ Of course, the same sort of thing may 


happen with an affirmative judgment, if it answers a 
question; you then say "y^^j ^^^ ^^ cheese". Here you really 


"the statement *this is cheese' is true" 

; and when you say 
"this is not cheese" you mean "the statement *this is cheese' is 
false". In either case, you are speaking about a statement, which 
you are not doing in a direct judgment of perception. The man, 
therefore, who understands only object- words, will be able to 
tell you everything that is in the larder, but will be unable to 
infer that there is no cheese. He will, moreover, have no concep- 

tion of truth or falsehood; he can say "this is butter" but not 
"it is true that this is butter". 

The same sort of considerations apply to "all" and "some". 
Suppose our unphilosophical observer goes to a small Welsh 
village in which every one is called Williams. He will discover 
that A is called Williams, B is called Williams, and so on. He may, 
in fact, have discovered this about everybody in the village, but he 
cannot know that he has done so. To know it, he would have to 

know "A, B, C, 

... are all the people in this village". But this 
is like knowing that there is no cheese in the larder; it involves 
knowing "nobody in this village is neither 



nor . 



And this is plainly not to be known by perception 

The case of "some" is a little less obvious.* In the above case 


will not pur friend know that "some people in this village are 

called Williams"? I think not. This is like "pudding-or-pie". 

From the standpoint of perception, none of them are 




they are the people they are. 



through language that we can understand 







Whenever we make a statement about some of a collection, there 
are alternative possibilities in our minds ; in each particular case, 
the statement may be true or false, and we assert that it is true in 
certain cases but perhaps not in all. We cannot express alter- 
natives without introducing truth and falsehood, and truth and 



ic, again, will be resumed in a later chapter, 



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Dod as we have seen, are linguistic terms. A pure object 



therefore, cannot contain the word "some 

any more 

he word "all**. 

, have seen that the object-language, unlike languages of 

orders, does not contain the words " 









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■f sense whatever. The next stage in language is that in 
I we can not only speak the object-language, but can speak 
it. In this second-type language, we can define what is 
: by saying, of a sentence in the first-type language, 
t is true. What is meant is that the sentence must mean 
:hing that can be noticed in a datum of perception. If you 

dog and say "dog", you make a true statement. If you see 
in a kennel and say "dog in kennel", you make a true state- 
There is no need of verbs for such sentences, and they may 

St of single words. 

le of the things that have seemed puzzling about language 

in ordinary speech, sentences are true or false, but single 

s are neither. In the object-language this distinction does not 

Every single word of this language is capable of standing 

means that it is applicable to 
resent datum of perception. In this language, when you say 


, and, when it stands alone 

;", your statement is false if it is a wolf that you are looking 
_ ordinary speech, which is not sorted out into languages of 
'ent types, it is impossible to know, when the word "dog" 
's by itself, whether it is being used as a word in the object- 

aage or in a linguistic manner, as when we sav 


that is not a 

. Obviously, when the word "dog" can be used to deny the 
met of a dog as well as to afHrm it, the single word loses all 



which all 

tive power. But in the object-language 
•s are based, every single word is an assertion. 
2t us now re-state the whole matter of the object-language, 
n object-word is a class of similar noises or utterances such 
from habit, they have become associated with a class of 
ially similar occurrences frequently experienced at the same 

as one of the noises or utterances in question. That is to 

let A 




be a set of similar 








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a^^a^^a^ . • • be a set of similar noises or utterances; and supposr 
that when Ai occurred you heard the noise a^^ when Ag occurred 
you heard the noise a^, and so on. After this has happened a 
great many times, you notice an occurrence A^ which is like 

I, Agj A3 . , ., and it causes you, by association, to utter or 

imagine a noise a^ which is like a^, a^, a^ . , * If, now, A is a 
class ofmutually similar occurrences ofwhichAi,A2 J A3 - . . a„ 
are members, and a is a class of mutually similar noises or utter- 
ances of wliicli (3]., a^, a^^ . . , an are members, we may say that 
cr is a word whicli is tlie name of the class A* or **means** 

class A. This is more or less vague, since there may be several 

classes which satisfy the above conditions for A and a. A child 
learning the object-language applies Mill's Canons of Itiduction, 
and gradually corrects his mistakes* If he knows a dog called 
"Caesar", he may think this word applies to all dogs. On the 
other hand, if he knows a dog whom he calls **dog", he may not 
apply this word to any other dog. Fortunately many occurrences 
fit into natural kinds; in the lives of most children, anything that 
looks like a cat is a cat, and anything that looks like one's mother 
is one's mother. But for this piece of luck, learning to speak would 

be very difficult. It would be practically impossible if the tem- 
perature were such that most substances were gaseous. 

If now, in a certain situation, you are impelled to say *'cat", 
that will be (so long as you are confined to the object-language) 
because some feature of the environment is associated with the 
word "cat", which necessarily implies that this feature resembles 
the previous cats that caused the association. It may not resembk 
them sufficiently to satisfy a zoologist; the beast may be a lynx 
or a young leopard. The association between the word and the 
object is not likely to be "right" until you have seen many animals 
that were not cats but looked rather as if they were, and many 

other animals that were cats but looked rather as if they were 
not. But the word "right", here, is a social word, denoting correct 
behaviour. As soon as certain beasts suggest the word "cat" 
to you and others do not, you possess a language, though it 

may not be correct English. 



Theoretically, given sufficient capacity, we could express in 
the object-language every non-linguistic occurrence. We can 
in fact observe fairly complicated occurrences, such as '*while 
John was putting the horse in the cart, the bull rushed out and I 
ran away", or "as the curtain was falling, there were cries of 
*fire' and a stampede". This sort of thing can be said in the 
object-language, though it would have to be translated into a 
sort of pigeon English. Whether it is possible to express in the 
object-language such observable facts as desires, beliefs, and 
doubts, is a difficult question, which I shall discuss at length 
in a later chapter. What is certain is that the object-language 
does not contain the words "true" and "false", or logical words 
such as "not", "or", "some", and "all". Logical words will be 
the subject of my next chapter. 






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In the 

present chapter I wish to consider 

certain words wh 

nn^V?!,*' S'"""?''^ language and in all higher languages 
not in the object-language. The words " ^ 

teristic of logic. I shall especially consider "true 


m question are char; 

"or", "some" 




^ — „ — ^ --w*wAv*v.A tiuc J laise no 
air'. We know from logic that thesp tPr 

S^ht "f"? «»«i in -erms of which. Our probi™ S 

propositions in which they occur 

way m which we come 

to knc 

Let us begin with the words "true". *'false", and 

unnecessary to have the two words *YaIse" and ^*not» 



• ..* 


for, if 

in the object you say "not-/', but if in the 

js a proposition '> is false" and "not-/' are strictly synonymot 
> is false". If you want butter' and b Jk iTa SJS ^ fir 

^eam cheese, you will say "this isn't butter- but T±T^ 
man offers for sale a substance labelled "butte 

to be margarine, you will say 




which you fin 

because you are more interested 


in his goods. Such rhetorical ^ 

us, and we may safely treat ^Talse" and 

you say this is butter, but that 

in his wickedness tha 

points^ however, do not 


"not" as synonyms 

of !he owtT^ "^'^'' ^' ^^ '^^"'^""^J ^^ rf^e word 

for in Aat ;i;;^?^K' "°i1"P^y ^ "°^^ ''^ ^°*^"y "movements 
for in that respect they belong to the object-lan^age, but . 

with the rela- 
on the one 


having meaning We are concerned, that is to say, 
tion between object-words and object-sentences 
hand, and what they designate or Uert on the other 



"Word'* cannot occur in the object-language, but *'object-word" 
can occur in the secondary language. Assunming that logical 
words occur in the secondary language, "logical word" will first 
occur in the tertiary language. If "tertiary words" are defined 
as those that occur in the tertiary language but not in the primary 
or secondary language, then "tertictry word" belongs to the 
quaternary language. And so on. It is to be understood that each 
language contains all the languages of lower orders. "Word" is, 
itself, of ambiguous order, and has therefore no definite meaning ; 
if this is forgotten, contradictions are apt to result. Take 

3 ^*&'> 

the contradiction about "heterological". A predicate is "hetero- 
logical" when it cannot be predicated of itself; thus "long" is 
heterological because it is not a long word, but "short" is homo- 
logical.* We now ask: is "heterological" heterological.^ Either 

answer leads to a contradiction. To avoid such antinomies, the 
hierarchy of languages is essential. 

The words "true" and "false", as we are to consider them in 
this chapter, are to be applied only to sentences in the primary 


In practice, as opposed to philosophy, we only apply the words 
"true" and "false" to statements which we have heard or read 
or considered before we possessed the evidence that would enable 
us to decide which of the two words was applicable. Some 
one tells us that Manx cats have no tails, but as he has previously 
told you that Manx men have three legs, you do not believe him. 
When he shows you his Manx cat you exclaim, "so what you 

said was true!" The newspapers, at one time, said that I was 

dead, but after carefully examining the evidence I came to the 
conclusion that the statement was false. When the statement comes 
first and the evidence afterwards, there is a process called "veri- 
fication", which involves confrontation of the statement with the 
evidence. In the case of a statement in the primary language, th^ 
evidence must consist of a sensible experience or of a set of such 
experiences. We have already considered sentences describing 

* German, learned, beautiful are heterological: English, erudite, ugly are 



experiences. Speaking broadlvi the process of verification is as 

follows: first you hear or read or comider a sentence S; then 

you have an experience E; t!jen you observe that S is a sentence 
which describes E. In that case you say that S is **true**- 1 do not 
mean that this is a definition of the word **tnie'*j but that it i$a 
description of the process by which you come to know that this 

word is applicable to a given primary t^entence, Tlie word **fa!se*' 

is much more difficult* But before considering this word there 

are some further ihingn to be said about the word **tnie 


In the first place^ the word **trae*' may be applied to a sentential 
utterance,, a sentence, or a proposition. Two sentential yttexances 
which are instances of the same sentence^ or two sentences whidi 
are instances of the same proposition, are either both true or both 
false. Thus in determining truth or falsehood^ ir is tfie proposition 
that is relevant. 

In the second place, a sentence or proposiiion is known to be 
*'true'' when it has a certain relation to an experience* In the 
case of ^"verification*'^ the sentence comes first and the experience 
after, but this is logically irrelevant; if the experience coma fitstj 

it equally proves tlie sentence to be true, provided the sentence 

experience. What is tmmtt by this word 

**dcscribes*' we have already considered, and I shall say no mote 
about it at present. 

In the third place> not all sentences in the primary language 


can be correcriy said to describe a single experience* If you see 

something and say **that is a dog**, you are going beyond what 

can be seen at the moment. A dog has a past and a (umm^ it h^ 

auditory and olfactory characteristics, and so on. All these ate 
suggested by the word **dog*', whicli is a condensation of many 

inductions. Fortunately, animals fit into natural kinds. If yout 
dog proceeded to mew like a cat, and to give birth to a mixed 
litter of puppies and kittens, words would fail you. In like matmar 

the man who mistakes salt for sugar is making an induction 


what looks like this tastes sweet". In this case the induction is 
false. If he said merely "this is white", he would not be makiw a 

mistake. Even if he said "this is grey" because he meant by "grey" 



what other people mean by ^*white**, he would not be making an 
intellectual error, but only using language in an unusual way. 
So long as a man avoids words which are condensed inductions, 
and confines himself to words that can describe a single ex 
perience, it is possible fox a single experience to show that his 

words are true. 
When I say tliat such a word as **dog' 



inductions, I do not mean that such inductions are conscious or 
deliberate* Certain situations staggest the word **dog** to you, 

and both they and the word rouse certain expectations* When 

you have said **that is a dog", subsequent events may 
you; but when you have said **that is white*', nothing in your 
statement gives any ground for surprise at what happens next, or 
for supposing that you %verc mistaken in saying that what you 

saw was white* So long as your words merely 

experiences, the sole possible errors are linguistic, and these only 

involve socially wrong behaviour, not falsehood 

I come now to falsehood and negation, which raise some rather 

difficult problems. 

We have agreed that when you do what a logician would call 

**as$erting not-/?**, you are saying **/? is false'*. The question that 

am concerned with at present is: how can experience show 

you that a proposition is false? Let us take some very simple 
negation, such as **this is not white'** You say this, we will suppose, 
in the course of a discussion with the laundry* The phrase **ihis 
is white" is in your mind, this is before your eyes, and **this is 
grey'* is a sentence describing your experience. But **th5s is not 
white** is not a sentence describing what you see, and yet, on the 
basis of what you see, you are sure that it is true, in other words 
that "this is wlnte'* is false- It might be argued that you know the 
general proposition **what is grey is not white**, and that from 
this, together with **this is grey**, you infer **this is not white*' 
Or it might be said that you can confront the word **white** with 
what you see, and perceive an incompatibility. Either view has 


Let us first be clear on a point of logic. From premisses none 


* , 







of \vhich contains the word "not** or the word "false" (or some 
equivalent) it is impossible logically to infer any proposition 
containing either of these words. Therefore, if there are negative 
empirical propositions, there must be, among basic propositions, 
either pure negations, such as "this is not white'*, or implications 

of the form */? implies not-y ''? e.g. **if this is grey it is not white". 


Logic allows no third possibility. 

We certainly know — though it is difficult to say how we 
know — that two different colours cannot coexist at the same place 
in one visual field. Position in the visual field is absolute, and 
may be defined by relation to the centre of the field by means of 



two angular coordinates which we may call 0, <f>. I am saying that 
we know the following proposition: "at a given time and in a 

given visual field, if the colour A is at the place &, (f>y no other 

colour B is at this place". More simply: "this is red" and "this 
is blue" are incompatible. 

The incompatibility is not logical. Red and blue are no more 
logically incompatible than red and round. Nor is the incom- 

patibility a generalization from experience. I do not think I can 
prove that it is not a generalization from experience, but I think 
this is so obvious that no one, nowadays, would deny it. 

Some people say the incompatibility is grammatical. I do not 
deny this, but I am not sure what it means. 

There are other sets of sensible qualities that have the same sort 
of incompatibility as colours have. A sensation of touch on the 
toe has a quality which enables us to refer it to the toe; a sensation 
of touch on the arm has a quality which enables us to refer it to 
the arm. These two qualities are incompatible. "Hot** and "cold", 
"hard" and "soft", "sweet" and "sour", are similarly inconn- 
patible as applied to sensible experiences. In all these cases we 

see" the incompatibility. So much so that it requires some 
reflection to realize that an incompatibility such as that of "white" 
and "black" is not logical. 

If we regard such incompatibilities as among basic propositions, 
we have to suppose that we know basic general propositions of 
the form: "for all possible values of x^ <f>x implies not-i/^x". 






Here 'V' ^^Y ^^ "-^ ^s blue", and *V^" may be ''x is red''. In 
that case, given a judgment of perception "this is blue", we can 
infer "this is not red'*. We thus arrive at a negative empirical 
proposition, but by the help of a general proposition which is 
not empirical. 

This is not a very plausible or satisfying theory. We may say, 
instead, that whenever we perceive "this is blue", we can know, 
as a basic proposition, "this is not red". But I am not sure that 
this would help us much. For we must ask: how do we know 

that we can know this.^ It hardly seems to be an induction; it 
cannot be a logical inference. We shall therefore be driven to 
adopt a basic proposition even more complicated than the 
former one, namely: "whoever sees red, and asks himself 'is 
this blue?' knows that the answer is *no'." 

shall return to this problem in connection with basic pro- 
positions. For the present, I will leave it unsolved. 

I come now to the word "or", and again I am concerned with 
the circumstances in which we know propositions containing 
this word, without knowing which alternative is the right one. 

Disjunctions, as we have seen already, arise in practice in the 
form of a choice. You see a sign-post saying "To Oxford", and 
presently you come to a fork in the road where there is no sign- 
post. You then believe the proposition "Oxford is along the 
right-hand road or Oxford is along the left-hand road". It is in 
situations of this sort that disjunctions occur in practice. 

It is obvious that nothing in the non-linguistic or non-psy- 
chological world is "indicated" by a disjunction- Suppose that, 
in fact, Oxford is to the right: this is not something verbal, it is a 
fact of geography, and if you go to the right you will get there. 
Similarly if, in fact, Oxford is to the left. There is not a third 
possible location, "right-or-left". Facts are what they are^ with- 
out ambiguity. If a disjunction "/? or y" is true, it is true because 
p is true, or it is true because q is true; if/? and q both belong to 
the primary language, **p or q* is true in virtue of a fact which is 
"expressed" by />, or in virtue of a fact which is "expressed" by y. 
Thus "or" lives in the world of propositions, and catmot form 


part of any language in which, as in the primary language, every 
word is directly related to an object, or to a set of objects, which is 
its meaning. 

Psychologically, "or" corresponds to a state of hesitation, A. 
dog will wait at a fork in the road, to see which way you are 
going. If you put crumbs on the window-sill, you can see birds 
behaving in a manner which we sliould express by: "shall I 


brave the danger or go hungry?" I once, to test the story of 
Buridan's ass, put a cat exactly half way between her two kittenSj 
both too young to move: for a time she found the disjunction 
paralysing. I think that animals in a state of hesitation, although 
they do not use words, have something more or less analogous 
to a "propositional attitude", and I think any valid psychological 
explanation of the word *'or" must be applicable, with suitable 
adaptations, to any behaviour that shows hesitation- 
Hesitation arises when we feel two incompatible impulses 
and neither is strong enough to overcome the other* 


Thou*dsi shun a bear, 

But if thy flight lay toward the raging sea 
Thou'dst meet the bear i' the mouth. 


But if the sea was not very raging, you might be left in complete 
doubt as to which was worse; you would have, one might say, 
a disjunction in your body, not only in your mind 

will be remembered that we considered all speech to _ . 
fundamentally imperative: that is to say, it is designed to cause 
certain behaviour in the hearer. When "those behind cried Tor- 
ward', and those before cried 'back' ", the result upon people in 
the middle was a disjunction, in the sense in which animals may 

experience it, tor instance tigers in a hunt when surrounded by 
beaters. It is not really necessary that there should be outsiders 
to cry "forward" and "back". You can yourself have both motor 
impulses, and if you are used to words these impulses will suggest 
both words; you will then have a proper verba! disjunction, 
inanimate matter, when subjected to two simultaneous forces, 
chooses a middle course, according to the parallelogram law; but 



animals seldom do this. No motorist, at a fork in the road, goes 
across the fields in the middle. As with motorists, so with other 
animals, either one impulse completely prevails, or there is 
inaction. But the inaction is quite different from that of a quiescent 
animal : it involves conflict and tension and discomfort ; it is not 
genuine inaction, but search for some way of reaching a decision, 

disjunction is the verbal expression of indecision, or, if a 
question, of the desire to reach a decision. 

Thus when some one asserts */? or (jf'\ neither/? nor q can be 
taken as saying something about the world, as would be the 
case if we asserted one of the alternatives ; we have to consider 
the state of the person making the assertion. When we assert /?, 
we are in a certain state ; when we assert q^ we are in a certain other 
state; when we assert **/? or q* we are in a state which is derivative 
from these two previous states, and we express this state, not 
something about the world. Our state is called "true" if/? is true, 
and also i£q is true, but not otherwise; but this is a new definition. 

But, it will be objected, if we know "/? or q'\ surely we know 
something about the world ? To this question we may answer ye^ 
in one sense and no in another. To begin with the reasons for 
answering no : when we try to say what we know, we must use 
the word "or'' over again. We can say: in a world in which/? 
is true, "/> or /' is true; similarly ii q is true: in our illustration 
of the fork in the road, "this road goes to Oxford" may express 
a grographical fact, and then "this road or that goes to Oxford" 
is true; similarly if that road goes to Oxford; but there is no state 
of affairs in the non-linguistic world which is found when, and 
only when, this road or that goes to Oxford. Thus the straight- 
forward correspondence theory of truth, which is valid in the 
primary language, is no longer available where disjunctions are 

Here, however, there is a difficulty which must be examined, 
which brings us to the reasons for the opposite answer to our 
question. Often a single word is logically equivalent to a dis- 
junction. The following conversation might occur between a 
medical logician and his wife. "Has Mrs. So-and-So had her 





child ? 



it a boy or a girl?*' "Yes 


though logically impeccable, would be infuriating* One 

The last answer 


say "a 

child is never a boy-or-girl, but only one of the alter 

For certain purposes, propositions containing the word 
"child" are equivalent to the same propositions with the words 
"boy or girl" substituted for "child"; but for certain other pur- 
poses the equivalence fails. If I am told "Mrs. So-and-So has 

had a child", I can infer that she has had a boy or a girl But i 

• I do not 

I then want to know whether she has had a boy or a 

want to know whether she has had a child, since I know this 


In this question, it is necessary to separate 

logic. When, in daily talk, we use 

the word **or" 



we do so^ as 

a rule, because we are in doubt and wish to decide an alternative 
If we have no wish to decide the alternative, we shall be content 


with a generic word covering both possibilities- If you are to 
inherit Mrs. So-and-So's money provided she dies childless, you 
will be interested in the question whether she has had a child 
but only politeness will impel you to ask whether it is a boy or 
a girl. And clearly you know, in some sense, something about 
the world when you know a child has been born, even thouiih 

you do not know its sex 



distinction* and if so .what, between disjunctive 


predicates and others? If "A" and "B" are two predicates 

is logically equivalent to "A-and- 





-and-not-B*% Thus so 

far as logic is concerned, any predicate can be replaced by a dis- 
junction. From the psychological point of view, on llie other 
hand, there is a clear distinction. A predicate is disjunctive if we 

feel a desire to decide alternatives which it leaves open; if not, 

is not. But this is not quite adequate. The alternatives must be 

such as the predicate itself suggests, not irrelevant possibilities, 



is not to be considered disjunctive because it leaves 

open the question "dark or fair?" Thus a predicate is only dis 
junctive if it suggests a question, and whether it does so or not 
depends solely upon the interests of the person concerned. 
All our knowledge about the world, in so far as it is expressed 





in words, is more or less general, because every sentence contains 
at least one word that is not a proper name, and all such words 
are general Consequently every sentence is logically equivalent 
to a disjunction, in which the predicate is replaced by the alter- 
native of two more specific predicates. Whether a sentence gives 
us a feeling of knowledge or of doubt depends upon whether it 
leaves open alternatives calling for dijflferent actions and emotions 
or not. Every disjunction which is not logically exhaustive (i.e., 
not such as ^*A or not-A") gives some information about the 
world, if it is true; but the information may leave us so hesitant 
as to what to do that it is felt as ignorance. 

Owing to the fact that words are general, the correspondence 
of fact and sentence which constitutes truth is many-one, i-e., 
the truth of the sentence leaves the character of the fact more or 
less indeterminate. This indeterminateness , can be diminished 
without limit; in the process of diminishing it, former single 
words are replaced by disjunctions. "This is metal" may satisfy 
us for some purposes; for others, such a statement must be re- 
placed by "this is iron or copper or, etc.", and we must seek 
to decide which possibility is realized. There is no point in the 
growing precision of language beyond which we cannot go; our 
language can always be rendered less inexact, but can never 

become quite exact. 

Thus the difference between a statement which is disjunctive 
and one which is not does not consist in any difference in the 
state of affairs which would make it true, but solely in the question 
•whether the difference between the possibilities which our state- 
ment leaves open is interesting to us or not. 

There is another situation in which a disjunction may arise in 
practice, and that is where there is imperfect memory. "Who 
told you that ?** "Well, it was either Brown or Jones, but I can t 
remember which.'* "What is So-and-So*s telephone number? 

I know it is 5x4 or 541, but I can't be sure which is right without 
looking it up/* In such cases, there was originally an experience 
which gave rise to a judgment of perception, in which there was 
no disjunction; and if you were to set to work to find out the 






truth, you would prove one of the alternatives, and again there 
would be no disjunction, Basic propositions, when they are 
expressions of present experience, never contain the word "or** 
unless the experience is verbal; but memories may be disjunctive. 

We come now to propositions containing the word "some" 
or the word "all". We considered these, in the previous chapter, 
to the extent required to satisfy ourselves that they could not be 
included in the primary language, but we want now to consider 
them more positively, and particularly to consider the circum- 
stances that lead us to make use of such propositions. 

Propositions about "some" arise, in practice, in four ways: 
first, as generalizations of disjunctions; secondly, when, having 
come across an instance, we are interested in the compatibility 
of two general terms which might have been thought incompatible ; 
thirdly, as steps on the way to a generalization; and fourthly, in 
cases of imperfect memory analogous to those that we considered 
in connection with disjunction. Let us illustrate these successively. 

In our former illustration of the road to Oxford. iL instead of 

) **> 

a mere fork, we had come to a place where a great many roads 
branched off, we might have said: "well, some road must lead 
to Oxford". Here the alternatives can be enumerated, and we have 

merely an abbreviation of a disjunction "p or y or r or 




where/?, ^,r, . . . can all be collected into one verbal formula 

The second kind of case is more interesting. It is illustrated by 
Hamlet, when he says: "one may smile and smile and be a 
villain; at least I am sure it may be so in Denmark". He has dis- 

covered a person (namely the King) who combines smiling with 
villainy, and has arrived at the proposition: "at least one villain 
smiles". The pragmatic value of the proposition is: ''mn time I 
meet a man who smiles and smiles, I will suspect him of villainy". 
He does so in the case of Rosencrantz and Gildenstern, Similar to 
this are the propositions "some swans are black" and "some 
blackbirds are v/hite"; they are warnings against plausible 
generalizations. We make such propositions when the generaliza- 
tion is more interesting to us than the particular instance — 
though in Hamlet's case this is an ironical pretence 



Tile third kind of case arises when we are trying to prove an 
incluctive generalization, and also when instances lead us to dis- 

a general proposition in mathematics. These cases are 
siixiilar, except that in the latter you arrive at certainty, and in the 

only at probability. Let us take the latter case first. You 





I +3 +S 





— - ** , and you say to yourself: "in some cases, the sum of the 
first 7t odd numbers is n^; perhaps this is true in all cases". As 
soon as this hypothesis has occurred to you, it is easy to prove 
that it IS correct. In empirical material, a complete enumeration 
may sometimes be possible. You discover (say) that iron and 
copper^ which are metals, are good conductors of electricity, and 
you suspect that this may be tme of all metals. In this case, the 
generalization has the same degree of certainty as the instances. 

" . and C died, and were men, therefore 



But -when you argue : " A 

some men are mortal; therefore perhaps all men are mortal 
you cannot make your generalization as certain as its instances 
both because you cannot enumerate men and because some have 
not yet died. Or take a cure for a disease which, so far, has only 

tried in a few cases, but in all of them has proved bene- 
ficial; in this case a proposition about some is very useful as 
suggesting the possibility of a proposition about all 


regard to imperfect memory 
analogous to those of disjunctions 

the instances are closely 
I know that book is some- 

where in my shelves, because I saw it yesterday 


I dined with 

B who made a most admirable joke, but unfortunately I have 

Mr _ ^ . 

forgotten it.'" "There are some very good lines m The Excursion 

but I can't remember any of them." Thus a great deal of what we 
know at any given time consists of propositions about sorm 
which we cannot, at the moment, deduce from propositions with 

singular subjects, nor yet from propositions about all. 

A statement about some has, as our four kinds of instances have 
shown, three kinds of uses : it may be a step towards the proof of 
a prop osition with a singular subject, or towards the prooi ot 
a general proposition, or it may be a refutation of a contrary 
generalization. In the first and fourth classes of cases, the pro- 


position about some is intended to lead on to a proposition with 
a singular subject: ^'thts is the road to Oxford*' or ^'here is that 
book" (where 1 take here as the subject). There is this difference 
between the first and fourth classes of cases, that in the first the 
proposition about some is always an inference, whereas in the 
fourth it is not. In the second and third classes of cases, the pro- 



some S is P" is deduced from instances "S 





"S2 is P", etc. ; it tells us less than they do, but tells us the part 
that is useful for the purpose in hand. 

What exactly do we know when we know a proposition of the 
form "some S is P" without knowing either "all S is P'* or some 

proposition of the form "Si is P" } Let us take as our example 
"t know that book is somewhere in this room". There are two 
circumstances which would logically justify you in saying this 
though in neither case would you say it unless you were a pro 
fessional logician. The first would be 
with that book — say 



room were 


a publisher's room, completely stacked 
with copies of a certain best seller. You could then say: "every 
place in this room contains the book in question, therefore (since 
the room exists) some place contains it*\ Or you might be seeing 
the book, and argue: "this place contains it, therefore some place 

contains it" " 

But in fact, unless you were engaged in teaching 

you would never argue in this way. When you say "that 
book is somewhere in this room", you say so because you cannot 
be more definite. 

It is obvious that "the book is somewhere in the room" cannot 
be a judgment of perception; you cannot perceive somewhere^ 
you can only perceive there. But a judgment of memory is different. 
You may remember "I saw the book when I was in this room", 



mething of that kind. You may remember saying 

there's that book" while you were in the room. Or you may have 
a pure verbal memory of saying "I see I did put that book on a 
shelf". These, however, are only the grounds for your judgment • 
they are not an analysis of it. 

The analysis of such a judgment must be essentially similar 
to that of a disjunction. There is a state of mind in which 





perceive "the book is in this place", another in which you per- 
ceive **the book is in that place", and so on. The state of mind 
when you judge "the book is somewhere in the room" contains 

"^hat all these have in common, together with perplexity. It is 
because of the absence of perplexity that you would not make 
the judgment in the above two cases in which it could be deduced 
from more definite judgments. To this, however, there is an 
exception : if you have doubted whether the book is in the room, 
and then you see it, you may say "so the book is in the room". 
This is no longer our present case, but that of the smiling villain. 

In the 

case of a judgment about somcy as in disjunction, we 
cannot interpret the words except in reference to a state of mind. 
We cannot, in fact, ever so interpret our words except in the 
primary language. 

Most of what we have said about "some" applies also to "all". 



is, however 

"some", and they 

, an important difference in regard to know 
ledge. "We often know propositions about 
can be proved empirically, although they cannot express facts 
of direct observation. But propositions about "all" are much 
more difficult to know, and can never be proved unless there are 
some such propositions among our premisses. Since there are 
no such propositions among judgments of perception, it might 
be thought that we must either forgo all general propositions 
or abandon empiricism. Yet this seems to contradict common 

Take an instance we have already discussed, "there is no 
cheese in the larder". It seems preposterous to maintain that 

we accept statements of this sort, we abandon 



take another instance we have already discussed, "every one in 
this village is called Williams", arrived at by complete enumera- 
tion* There is, however, a difficulty, which is illustrated by Ham- 
let's mother when he'asks if she does not see the ghost: 

Hamlet: Do you see nothing there ? 
Queen: Nothing at all; yet all that is I see. 

have always wondered how she knew she saw "all that is" 
But she was right in regarding this as a necessary premiss for her 



denial of the ghost; and so it is for the man who says there is no 
cheese in the larder, and nobody in the village not called Williams, 
Clearly the question of our knowledge of general propositions 
involves difficulties as yet unsolved. 

J am not at all sure that empiricists are right when they reject 
from among basic propositions all extra-logical general state- 
ments. "We have already considered the statement "no visual 
place contains two different colours", which seems to be a case 
in point. Or, to take an even more inescapable Instance, suppose 
you live in a remote country place, and you are expecting the 
arrival of a friend in a car. Yourwife says "do you hear anything 
and after listening for a moment you answer "no". Have you, in 
giving this answer, abandoned empiricism.'* You have com- 
mitted yourself to a stupendous generalization, namely : * 'every- 
thing in the universe is not a sound now heard by me". And yet 
no one can maintain that experience does not justify your state- 


ment. I think, therefore, that, apart from logic, we do know 
some general propositions otherwise than by inductive general- 
ization. This, however, is a very large question. I shall return to 
it in a later chapter; for the moment, I only wish to enter a caveat. 
The question arises : do logical words involve anything psy- 
chological.^ You may see something, and say "this is yellow"; 
afterwards you may say "it was yellow or orange, but I can't 
remember which". One has a feeling that, in such a case, the 
yellow was a fact in the world, whereas "yellow or orange" 
could only exist in someone's mind. It is extremely difficult to 

avoid confusion in considering this question, but I think what 
can be said is this: The non-mental world can be completely 
described without the use of any logical word, though we cannot, 
without the word "all", state that the description is complete; 
but when we come to the mental world, there are facts which 

cannot be mentioned widiout the use of logical words. In the 

above instance, I remember that it was yellow or orange; in a 
complete description of the world, this recollection must be men- 
tioned, and it cannot be mentioned without using the word "or" 
or some equivalent. Thus while the word "or" does not occur in 



the basic propositions of physics, it does occur in some of the 
basic propositions of psychology, since it is an observable fact 
that people sometimes believe disjunctions. And the same is true 
of the words **not", "some", and "all*'. 

, w^**xv. , 

If this is true, it is important. It shows, for instance, that we 
cannot accept one possible interpretation of the thesis which 
Carnap calls "physicalism", which maintains that all science can 
be expressed in the language of physics. It might, however, be 
contended that, in describing what happens when a man believes 
"/? or q\ the "or" that we must use is not the same as the "or" 
of logic. It is possible to contend, more generally, that when we 
assert "A believes /?", the p is not the same as when we assert 
* jo", and that the difference ought to be indicated by writing "A 
believes 'p ". If we were speaking of what A says, not of what 
he believes, we should certainly have to make this distinction. A 
says "fire", and we say "A says *fire' ".In what we say, "fire" 
occurs as denoting a word, whereas in what A says it occurs as 
denoting an object. This whole question is a very difiicult 
one, and I shall consider it in a later chapter in connection with 
propositional attitudes. Meanwhile, we must bear in mind that, 
prima facie^ logical words, though not necessary in describing 
physical facts, are indispensable for the description of certain 
mental facts. 



Chapter VI 

I ' 


iivntw^^-^j^. ,***»4-iff 

It is customary in logic to divide words into categories; names, 
predicates, dyadic relations, triadic relations, etc. This is not tlje 
total of words; it does not include lomcal words, and it is doubtful 

whether it includes wx)rds for '^propusitiunal attitudes*'^ such as 
**believe", *'desire*\ *'doubt". etc. There is also difficuhv about 


egocentric particulars", i.e. *T'', **this*\ "now'\ *1iere'\ etc. 

Propositional attitudes and egocentric particulars will be con- 
sidered in due course. For the present, it is names that I wish to 

To avoid verbiage, I shall speak of predicates^ when con- 
venient, as **monadic relarions**. Thus we are concerned with the 
distinction between names and relations, in regard to which we 
have to ask two questions: 

(i) Can we invent a language without the distinction of names 

and relations ? 

(2) If not, what is tlie minimum of names required in order 
to express what we know or understand? And, in connection with 
this question, which of our ordinary woixh are to be considered 



As to the first of these problems, I have very little to say. ft 
may be possible to invent a language witiiaut names, but for my 
part I am totally incapable of imagining such a language. This is 
not a conclusive argument, except subjeciively; it puts an end to 
my power of discussing the question. 

It is my purpose, however, to suggest a view which mi^ 
seem at first sight equivalent to the abolition of names. I propose 
to abolish what are usually called **particulars*\ and be content 


" The subjects of tliis chapter and the neixt will be rcsunwd in Chapter XXIV. 



'. ' 

1 1 


with certain words that would usually be regarded as universals 
such as *'red'\ *l3lue'\ *1iard'\ **soft'\ and so on. These words 



I shall suggest, are names in the syntactical sense; I am not there- 
fore seeking to abolish names, but to suggest an unusual extension 
for the word **name*'. 

Let us bedn with the definition of the word '*name*'. For this 

e we must first define **atomic forms*'. 
A sentence is of atomic form when it contains no logical words 
and no subordinate sentence. It must not contain *'or'\ **not 

5 **v^«- > 

**air', **some*' or any equivalent; nor must it be such as "I think it 
will rain'\ because this contains the subordinate sentence **it will 
rain". Positively, a sentence is of atomic form if it contains one 
relation-word (which may be a predicate) and tlie smallest 

number of other words required to form a sentence. If Rj is a 

predicate, R2 a dyadic relation, R3 a triadic relation^ etc. 

C-^)> HaC^,^), R 

IV^J> ^'^ZS^fJ/t *''3\'^> J^J Ul> 

# 4 « 

will be sentences of atomic form, provided x^y^ i are such words 

as make the sentences concerned significant. 
If Rft(,r|,.v2,x0, . . . ji«r„) is a sentence of atomic form, in which 
rt is an n-adic relation, x^^ xg, j^^, , • • x,i are names. We may 

define a **name** as any %vord that can occur in any species of 
atomic sentence, i.e. in a subject-predicate sentence, a dyadic- 
relation sentence, a triadic-relation sentence, and so on* A word 
other than a name, if it can occur in an atomic sentence, can only 

occur in an atomic sentence of one species; e*g* if R„ is an 

n-adic relation, the only species of atomic sentence in which 


can occur is llni^i^ ^2* -^3 * • • ^n)- A name can occur in an 

atomic sentence containing any number of words; a relation can 
only occur in combination with a certain fixed number of other 
words appropriate to that relation. 

This affords a syntactical definition of the word "name*** 
should be observed that no metaphysical assumptions are involved 
in the notion of **atomic forms*** Such assumptions only appear 

if it is assumed that the names and relations appearing in an 

f I I 




I ■ 



atomic sentence are incapable of analysis. In connection with 
certain problems it may be important to know whether our terms 
can be analysed, but ^in connection with names this is not im- 
portant. The only way in which any analogous question enters 
into the discussion of names is in connection with descriptions, 
which often masquerade as names. But whenever we have a 
sentence of the form 



"The X satisfying <f>x satisfies ^;c" 

we presuppose the existence of sentences of the forms "<^a'* and 
'*tl/a\ where * a" is a name. Thus the question whether a given 
phrase is a name or a description may be ignored in a funda- 
mental discussion of the place of names in syntax. For our pur- 
poses, unless reason should appear to the contrary, we may accept 
as a name whatever would ordinarily be considered as such: 
Tom, Dick, and Harry, the sun, the moon, England, France, etc 
But as we proceed it will appear that, even though such words 
be names, they are for the most part not indispensable for the 
expression of what we know. Per contra^ though some among 
indispensable words are, I believe, to be classed as names, these 
are, all of them, words not traditionally so classed. 

l^ames, prima facie, are of two sorts: those that, like the names 
mentioned in the last paragraph, designate some continuous 
portion of spacer time, and those that have an egocentric 
tion, such as "I", "you", "this", "that". Tliis latter class of words 
I propose to consider later; for the present, I shall ignore them 
We are concerned only, therefore, with such names as designate, 
without ambiguity in principle, some definite continuous portion 
of space-time. 

The first question to be considered is : how do we distinguish 
one region of space-time from another? This leads ultimately to 
such questions as: if there were in New York an Eiflfel Tower 
exactly like the one in Paris, would there be two Eiffel Towers, 
or one Eiffel Tower in two places .> If historv repeated itself 
would the worid be in two exacdy similar states on two different 
occasions, or would one and the same state occur twice, i.e.. 







precede itself? The answers to such questions are only partly 
arbitrary; in any case, they are indispensable for the theory of 
names . 

The theory of names has been neglected, because its impor- 
tance is only evident to the logician, and to him names can remain 
purely hypothetical, since no proposition of logic can contain 
any actual name. For theory of knowledge, however, it is im- 
portant to know what sort of objects can have names, assuming 
that there are names. One is tempted to regard **this is red" as a 
subject-predicate proposition; but if one does so, one finds that 

* this* * becomes a substance, an unknowable something in which 
predicates inhere, but which, nevertheless, is not identical with 
the sum of its predicates. Such a view is open to all the familiar 

objections to the notion of substance. It has, however, certain 
advantages in relation to space-time. If "this is red" is a pro- 
position ascribing a quality to a substance, and if a substance is 
not defined by the sum of its predicates, then it is possible for 
this and that to have exactly the same predicates without being 
identical. This might seem essential if we are to say, as we should 
like to say, that the supposed Eiffel Tower in New York would 
not be identical with the one in Paris. 

•wish to suggest that **this is red*' is not a subject-predicate 
proposition, but is of the form "redness is here"; that "red" is 
a name, not a predicate j and that what would commonly be called 
a "thing" is nothing but a bundle of coexisting qualities such as 
redness, hardness, etc. If this view is adopted, however, the 
identity of indiscemibles becomes analytic, and the supposed 
Eiffel Tower in New York would be strictly identical with the 
one in Paris if really indiscernible from it. This requires, when 
analysed, that spatial and temporal relations, such as to-the-lefi-of 
or Before, should not imply diversity. This causes difficulties in 
the construction of space-time as required in physics, and these 

difficulties must be overcome before the view that I am sug 

gesting can be considered a possible one. I think they can be 
overcome, but only by admitting as empirical and doubtful 
certain propositions which have seemed certain, such as "if A is 




to the left of B, A and B are not identical", where A and B are 

the nearest approach to "things" that our theory allows. 

Let us first establish a useful piece of vocabulary. Let us give 
the name "qualities" to specific shades of colour, specific degrees 
of hardness, sounds completely defined as to pitch and loudness 
and every other distinguishable characteristic, 






Although we cannot, in perception, distinguish exact from 
approximate similarity, whether in colour or in any other kind 

of quality, we can, by experience, be led to the conception of 

exact similarity, since it is transitive, whereas approximate 
similarity is not. Given a visual area, we can define its colour as 
the group of those visual areas which are similar in colour to it 
and to each other, and not all similar in colour to anything out- 
side the group.* In this definition, however, we have assumed 
that, if a given shade of colour exists in two visual areas, each 
visual area can be given a name ; we have, in fact, assumed the 
distinction of this and that^ apart from qualities, which we were 
intending to avoid. Let us, therefore, accept qualities as undefined 
terms for the present, and return later to the question of distin- 
guishing between two qualities so similar that they cannot be 

distinguished in immediate perception. 

Common sense regards a "thing" as having qualities, but not 
as defined by them; it is defined by spatio-temporal position, 
wish to suggest that, wherever there is, for common sense, a 

"thing" having the quality C, we should say, instead, that 


is to be replaced 


in question 

itself exists in that place, and that the 
by the collection of qualities existing in 
Thus "C" becomes a name, not a predicate. 

The main reason in favour of this view is that it gets rid of 
an unknowable. We experience qualities, but not the subject in 


which they are supposed to inhere. The introduction of 
unknowable can generally, perhaps always, be avoided by 
suitable technical 

devices, and clearly 

whenever possible. 

The main difficulty of the view that 

it should be avoided 

am advocating is as 


Cf. Camap's Logischer Aujbau der Welt. 


regards the definition of "place"* Let us see whether this difficulty 
can be overcome. 

Suppose we see simuhaneously two patches of a given shade 
of colour C ; let the angular coordinates of the one pate h in visual 

and those of the other d\ ^'. Then we are to say 

space be 

that C is at (fl, ^) and also at (6 



The angular coordinates of an object in the visual field may 

be regarded as qualities. Thus (C, 0, <^) is one bundle of qualities 



(C, e', 4>') 

is another. If we define 


as the bundle 

of qualities (C 

9 "> 


then we may say that this "thing" is at the 

place (0, <i>\ and it is analytic that it is not at the place {Q 



Let us extend this process to the construction of physical space- 
time. If I start from Greenwich with a good chronometer, or with 
a receiving set on which I receive a daily message at noon G.M.T., 

can determine my latitude and longitude by observation. 
Similarly I can measure altitude. Thus I can determine three co- 
ordinates which uniquely determine my position relative to 
Greenwich, and Greenwich itself can be defined by similar obser- 
vations. We may, for simplicity, treat the coordinates of a place 
as qualities; in that case, the place may be defined as being its 
coordinates. It is therefore analytic that no two places have the 

same coordinates. 

This is all very well, but it conceals the element of empirical 
fact upon which the utility of latitude and longitude depends. 
Suppose two ships ten miles apart, but able to see each other 

"We say that, if their instruments are sufficiently accurate, they 
will give different values for the latitude and longitude of the 

two ships. This is a question of empirical fact, not of definition 

for when I say that the ships are ten miles apart, I am saying 

something which can be proved by observations quite inde 
pendent of those that determine latitude and longitud 


metry as an empirical science is concerned with such observed 
facts as the following: if the distance between the two ships 


calculated from the difference of their latitude and longitude, we 
shall obtain the same result as if it is calculated by means of direct 

observations made of either ship from the other. All such observed 



I I 


facts are summed up by the statement that space is roughly 
Euclidean and that the surface of the earth is roughly spherical 

Thus the empirical element comes in when we explain the 
utility of latitude and longitude, but not in giving the definition. 
Latitude and longitude are connected by physical laws with other 
things with which they are not connected logically. It is empirical 
that if you can see that two places are a long way apart, they 
toU not be found to have the same latitude and longitude; this 
is what we should naturally express by saying that a place on the 
earth's surface is uniquely defined by its latitude and longitude. 

When I say that redness can be in two places at once, I mean 
that redness can have to itself one or more of those spatial rela- 
tions which, according to common sense, no '*thing" can have 
to itself. Redness may be to the right of redness, or above redness, 
in the immediate visual field ; redness may be in America and in 
Europe, in physical space. We need, for physics, something that 
cannot be in America and Europe at the same time; for physics, 
nothing can count as a "thing" unless it occupies a continuous 
portion of space-time, which redness does not. Nay, more: 
whatever occupies more than a point of space-time* must, for 
physics, be divisible into smaller "things". Our purpose is 
possible, to construct out of qualities bundles having die spatio- 
temporal properties that physics requires of "things". 

Latitude, longitude, and altitude are, of course, not directly 
observed qualities, but they are definable in terms of qualities, 
and it is therefore a harmless avoidance of circumlocution to call 
them qualities. They, unlike redness, have the necessary geo 



metrical properties. If 5, ^, h are a latitude, a longitude, and an . 
altitude, we shall find that the bundle (fl, ^, k) cannot be north 

or south or east or west or above or below itself, as redness can. 
If we defime a "place" by the coordinates (0, ^, A), spatial relations 

will have the properties we expect of them ; if we define it by 
such qualities as redness and hardness, it will not. 
So much for space— let us now consider time. 

In regard to time, we desire to find empirical objects such that, 
in regard to them, time shall be serial, that is to say, we desire to 




* r 




find a class definable in terms of observable objects, such that, if 
^y y? { ^^ »iembers of the class, we shall have : 

(i) ^ d-oes not precede x 


(2) if AT precedes y andy precedes {, then x precedes 7 


(3) if x: andy are different, either x precedes y ory precedes x 
We may, to begin with, ignore the third of these conditions 

which applies only to instants, not to events. The construction 
of instants as classes of events is a problem with which I have 
dealt else-^vhere. 

What -^w^e \vant is a class of events having a temporal unique 


ness analogous to the spatial uniqueness of latitude, longitude 
and altitdde. 

Artific ially ^ we can take the date and time of day as determined 
by an observatory. But here mistakes are possible; we want. 

possible, something less artificial* 

Eddington uses for this purpose the second law of thermo- 
dynamics. The drawback to this is that the law only holds of 
the universe as a whole, and may be false as applied to any finite 
volume; but only finite volumes are observable. While, therefore, 
Eddington* s method might be satisfactory for omniscience, it is 

more or less inadequate for us empirically. 

Bergson*s memory, if one could believe in it, would serve our 

< i| 

. According to him, nothing experienced is ever 
forgotten^ therefore my memories at an earlier date are a sub- 
class of my memories at a later date. My total memories at different 
times can, therefore, be serially ordered by the relation of class- 
inclusion, and the times can be serially ordered by correlation 
with the total memories. Perhaps memory could be used for our 


purpose -w^ithout the assumption that nothing is ever forgotten 
but I am. inclined to doubt this. In any case, memory is useless in 

relation to geological and astronomical time, which includes 

periods during which no memory is supposed to have existed. 

proceeding with the search for a class of events having 

the desired properties, let us consider a little more carefully 
what it is that we are supposing. We are supposing that there 



are only qualities, not also instances of qualities. Since a given 
shade of colour can exist at two different dates, it can precede 
itself; therefore "preceding" is not in general asymmetrical, but 
will be so, at best, in regard to some special kind of qualities or 

bundles of qualities. It is not logically necessary that any such 
kind should exist; if it does, that is a fortunate empirical fact. 

Many writers have imagined that history is cyclic, that the 
present state of the world, exactly as it is now, will sooner or later 
recur. How shall we state this hypothesis on our view ? We shall 
have to say that the later state is numerically identical with the 
earlier state; and we cannot say that this state occurs twice, since 
that would imply a system of dating which the hypothesis makes 
impossible. The situation would be analogous to that of a man 
who travels round the world : he does not say that his starting- 
point and his point of arrival are two diiSerent but precisely 
similar places, he says they are the same place. The hypothesis 
that history is cyclic can be expressed as follows : form the group 
of all qualities contemporaneous with a given quality; in certain 
cases the whole of this group precedes itself. Or : in these cases, 
every group of simultaneous qualities, however large, precedes 
itself. Such an hypothesis cannot be regarded as logically im- 
possible so long as we say that only qualities occur. To make it 
impossible, we should have to suppose a momentary subject of 
qualities, and to hold that this subject owes its identity, not to 
its character, but to its space-time position. 

The identity of indiscernibles, which follows analytically from 
our theory, is rejected by Wittgenstein and others on the ground 
that, even if a and b agree in all their properties, they may still 
be two. This assumes that identity is indefinable. Moreover it 
makes enumeration theoretically impossible. Suppose you. wish 
to count a collection of five objects A, B, C, D, E, and suppose 
tliat B and C are indistinguishable. It follows that, in the moment 

of counting B, you will also count C* and therefore 



conclude that there are four objects to be counted. To say that 




two, although they seem one, is to say 

something which, if B and C are totally indistinguishable, seems 



wholly devoid of meaning. Indeed, I should claim it as the prin 

cipal merit of the theory I am advocating that it makes the 
identity of indiscernibles analytic* 

Let us now return to the search for a set of qualities, or groups 
of qualities^ which has the properties required for constructing 
the time-series. I do not think this can be done without taking 
account of empirical laws ; it follows that it cannot be done with 
certainty. But so long as we are not in search of logical certainty, 
we can arrive at what is empirically sufficient by the means which 
w-e formerly rejected, e-g., memory and the second law of thermo- 
dynamics. Not all the causal laws with which we are acquainted 

reversible, and those that are not afford means of dating. It 
is easy to construct a clock which, in addition to showing hours 
and nninutes, will every day exhibit a number greater by one than 
that exhibited on the previous day. By such means we can make 
sure of having a complex of qualities which will not recur, at 
any rate while our civilization lasts. More than this we cannot 
knowj though we may find reason to think a large-scale exact 
recurrence very improbable. 

My conclusion is that qualities suffice, without our having to 
suppose that they have instances. Incidentally, we have reduced 
to the empirical level certain properties of spatio-temporal 
relations which threatened to be synthetic a priori general tmths. 

From the standpoint of theory of knowledge, there is still a 
question to be answered before our theory can be considered 
established. It is part of the larger question of the relation of 
conceptual precision to sensible vagueness. All science uses con- 

which are in theory precise, but in practice more or less 


vague. "One metre*' was defined with all possible care by the 
French Revolutionary Government : it was the distance between 
two marks on a certain rod at a certain temperature. But there 
were two difficulties : the marks were not points, and temperature 
cannot be determined exactly. Or take time-determinations, say 
midnight G.M.T. at the end of December 31, 1900, (The English 
thought this was the end of the nineteenth century, but they 
o ught to have substituted the meridian of Bethlehem for that of 







Greenwich.) Midnight can only be determined by observations, 
say of chronometers; but no observation is exact, i.e., there is a 
finite period of time during which any given chronometer will 
seem to point to midnight; and, moreover, no chronometer is 
exactly right. Therefore no one could know exactly when the 
nineteenth century ended. Two views may be taken of this 
situation : first, that there was an exact instant when the century 
ended ; second, that exactness is illusory, and that precise dating 
is even conceptually impossible. 

Let us apply similar considerations to the case of colours. 

which more directly concerns our present problem. I have sup- 
posed that a proper name should be given to each shade of colour^ 
but a shade of colour has the same kind of precision as an 

exact date or an exact metre, and can never be determined in 

There is a formal procedure which is applicable to all the cases 
in which we seek to derive, from something given in sense, a 
concept having an exactness that is no part of the datum. This is 


a device for passing from indistinguishahility to identity. Let 

stand for "indistinguishahility**. Then given two patches of 
colour, we may observe that the shade of one patch has the rela- 
tion S to the shade of the other. We can, however, prove that S 
does not imply identity, for identity is transitive, but S is not. 
That is to say, given three shades of colour x^ y, {, existing in 

three visible patches, we may have xSy and y S ^, but not xSi* 
Therefore x is not identical with i^ and therefore y cannot be 

identical with both x and ^, although it is indistinguishable from 

both. We can only say that x and y are identical if jc S { always 

implies y S 7, and vice versa. The precise shade of colour of x 

can now be defined as the colour common to all patches y 

which are such that whatever is indistinguishable in colour 

from X is also indistinguishable in colour from y, and vice versa, 

so that every patch is distinguishable from both x and y or from 

This reduces the determination of the precise shade of some 
given coloured patch to the collection of a number of data each 




of which can, in principle, be obtained from observation. 

ciifEcuky, now, is 









not in relation to any one of the requisite 

^^ but in relation to their multiplicity. Our definition supposes, 

^^ its second clause, that every patch of colour i can be compared 
"With every y that is indistinguishable from x. This is, in practice, 

sible, since it requires a complete survey of the visible 

past, present, and future. We can never know that two 

X and y are of the same shade, for, though every i that 

observed may have the relation S either to bodi or to 

a new { may always be found later for which this is not 



Consequently, if "C" is the name of an exact shade of 
no proposition of the form "C exists here" can ever be 



unless **C" is defined as "the shade that exists here". 

It: should be observed that difficulties of the same sort exist 

gard to all empirical concepts. Take, e.g., the concept 



\£ all the stages in the evolution of modem man were spread out 

us, there would be some specimens of which we should 





xirihesitatingly "that is a man", and others of which we should 
unhesitatingly "that is not a man"; but there would be inter- 
specimens concerning which we should be doubtful. In 
nothing that we can do to make our definition more 
precise will avoid this uncertainty. It may be that, in fact, at some 

in evolution there was such a great and sudden mutation 



] ustify us in giving the name * *man' * to what 



not to what went before, but if so this is a lucky accident, 
intermediate forms could still be imagined. In short, every 
empirical concept has the sort of vagueness that is obvious in 

examples as 






bald". Some men are certainly tall 


are certainly not tall ; but of intermediate men we should 

I shouldn't be inclined to 


think so," or "no 

him tall". This state of aflfairs is to be found, in a greater or 
degree, in regard to every empirical quality. 

consists largely of devices for inventing concepts 
Ixa^^ing a greater degree of precision than is found in the concepts 
of every-day life. The degree of precision possessed by a concept 


pable of exact numerical definition. Let "P(a:)" mean *'pc 





the predicate P". Let us survey all the known instances of things 

of the sort that might be expected to have the predicate 
suppose the number of such things to be n. Suppose that in m 
of these instances we can definitely assert "not-P(:v)". Then mjn 
is a measure of the precision of our concept P. Take for example 
measurement: the statement "the length of this rod exceeds or 
falls short of one metre" can, by scientific methods, be shown to 
be true except in a very small percentage of cases, but rough-and- 
ready methods leave a much larger percentage of doubtful cases. 



But now take "the length of this rod is one metre". 

never be proved, but it cannot be disproved in the cases in which 

our previous proposition cannot be proved. Thus the more pre 

cision we give to a concept, the oftener it can be proved to be 

inapplicable, and the seldomer it can be proved to be applicable. 

When it is completely precise, it can never be proved to be 


If "metre" is intended to be a precise concept, we shall have 
to divide lengths into three classes: (i) those certainly less than a 
metre; (2) those certainly greater than a metre; (3) those belonging 

to neither of the first two classes. We may, however, think it 
preferable to make "metre" an inexact concept; it will then mean 
"any length which, by existing scientific methods, is not distin 
guishable from that of the standard metre". In that case, we can 
sometimes say "the length of this rod is one metre". But the 
truth of what we say is now relative to existing technique ; an 
improvement in the apparatus of measurement may make it 


All that we have been saying about lengths applies, mutatis 
mutandzsy to shades of colour. If colours are defined by wave 
lengths, the argument applies word for word. It is evident that 
throughout, the fundamental empirical concept is indistinguish 
ability. Technical devices can diminish but not wholly remove the 
inexactness essential to this concept. 

We shall say: the colour of this given patch is to be called "C'\ 
Then the colours of all other patches are divided into two classes : 
(i) those diat we know to be not C; (2) those that we do not 


f m ^""i^ HI f 11 


t ' 







kno-w to be 


The whole purpose of methods of precision 




is to make the second class as small as possible. But we can never the point xvhere we know that a member of the second class 
nrnast be identica.1 "with C; all that we can do is to make the second 

olours more and more like C. 

at the following statement: I give the name 

ss consist o 


^We thus 

to the 


of colour that I see at the visual place 


ive the name 


*C"* to the colour at 




may be that 



and C are distinguishable; then they are certainly different. 

they are indistinguishable, but that there is a 



colour C ' ' 


guishable from one, but not from the other; in 

that case also C and C are certainly different. Finally, it may be 
tHat every colovir known to me is either distinguishable from both 




indistinguishable from both; in that case, C and C may be 
identical, i.e., * ' C* and "C" may be two names for the same thing. 
Bxxt since I can never know that 1 have surveyed all colours, 

can never be sure that C and C are identical. 


This answ^ers the question concerning the relation of con- 
ptual precision to sensible vagueness. 
It remains- however, to examine possible objections to our 

m I 


derived from what 



egocentric particulars'*. This 

^vill be done in the next chapter. 







1 ?*; 


/ ^ ^7 A' " i,Ji^*'^^^^*4^ i 

Chapter VII 


The words with which I shall be concerned in this chapter are 
those of which the denotation is relative to the speaker. Such are 

thisy that, /, you, here, there, now, then, past, present, future. Tense 

in verbs must also be included. Not only "I am hot", but "Jones 
is hot", hais a significance which is oxily determinate when we 
know the time at which the statement is made. The same applies 
to "Jones was hot", which signifies "Jones's hotness precedes 
the present", and thus changes its significance as the present 

All egocentric words can be defined in terms of "this". Thus: 

"I" means "The biography to which this belongs"; "here" means 

"The place of dbis"; "now" means "The time of this"; and so 

on. We may therefore confine our inquiry to "this". It does not 

seem equally feasible to take some other egocentric word as 

fundamental, and define "this" in terms of it. Perhaps, if we 

gave a name to "I-now", as opposed to "I- then", this name 

could replace "this"; but no word of common speech seems 

capable of replacing it. 

Before embarking upon more difficult questions, let us observe 

that no egocentric particulars occur in the language of physics. 

Physics views space-time impartially, as God might be supposed 

to view it; there is not, as in perception, a region which is specially 

warm and intimate and bright, surrounded in all directions by 

gradually growing darkness. A physicist will not say "I saw a 

table", but like Neurath* or Julius Caesar, "Otto saw a table"; 

he will not say "A meteor is visible now", but "A meteor was 

visible at 8h- 43m. G.M.T.", and in this statement "was" is 


See Chapter X. 




intended to be without tense- There can be no question that the 
non-mental world can be fully described without the use of 
egocentric words. Certainly a great deal of what psychology 

wishes to say can also dispense with them. Is there, then, any 
need for these words at all? Or can everything be said without 
them ? The question is not easy. 

Before we can investigate this question, we must decide 


we can, what is meant by the word "this", and why egocentric 
particulars have been found convenient. 

The word "this" appears to have the character of a proper 
name, in the sense that it merely designates an object without 

in any degree describing it. It might be thought to ascribe to 
an object the property of being present to attention, but this 
would be a mistake : many objects on many occasions are present 
to attention, but on each occasion only one is this. We may say : 
"this" means "the object of this act of attention"; but this 
obviously is no definition. "This" is a name which we give to 
the object to which we are attending, but we cannot define "this" 
as "the object to which I now attend", because "I" and "now" 
involve "this".* The word "this" does not mean: "what is in 
common among all the objects successively called *this*"; for 
on each occasion when the word "this" is used there is only one 
object to which the word applies. "This" is apparently a proper 
name which is applied to different objects on every two occasions 
when it is used, and yet it is never ambiguous. It is not like the 
name "Smith", which applies to many objects, but to each 
always; the name "this" applies to only one object at a time, 
and when it begins to apply to a new object it ceases to be 

applicable to the old one. 

We may state our problem as follows. The word "this" is 
one word, which has* in some sense, a constant meaning. But if 

, YVXXXWX X*«^, ^^ w^.r*w ww.^s,. 

we treat it as a mere name, it cannot have in any sense a constant 
meaning, for a name means merely what it designates, and the 
designatum of "this" is continually changing. If, on the other 

* Or, if we take "I-now" as fundamental, exactly the same problems will 
arise concerning it as those that otherwise irise concerning "this". 




hand, we treat "this" as a concealed description, e.g., "the object 
of attention", it will then always apply to everything that is ever 
a "this*', whereas in fact it never applies to more than one thing 
at n time. Any attempt to avoid this undesired generality will 
involve a surreptitious re-introduction of "this" into the definiens. 

this", which 

is con 

and throws doubt 

(There is yet another problem about * 
nected with the subject of proper names 

prima facie^ on the conclusion of the preceding chapter. If we 
see simultaneously two patches of a given shade of colour, we 
shall say: "this and that are precisely similar in colour". We 
shall have no doubt that one of them is this and the other that; 
nothing will persuade us that the two are one. This, however, 
is a puzzle that is easily resolved. What we see is not merely 
a patch of colour, but a patch in a given visual direction. If "this' 

means "a patch in such a direction" and "that" means "a patch 
in such another direction", these two complexes are different, 
and there is no reason to infer that the bare colour is twofold.) 

Is "this" a name, or a description, or a general concept .'^ To 
any answer there are objections. 

If I say that "this" is a name, I am left with the problem of 
explaining on what principle we decide what it names on dif- 
ferent occasions. There are many men called "Smith", but they 
do not share any property of Smithyness; in each case it is an 
arbitrary convention that the man has that name. (It is true that 
the name is usually inherited, but it can be adopted by deed-poll. 
A man's name is legally anything by which he publicly announces 
that he wishes to be called.) But it is not an arbitrary convention 
that leads us to call a thing "this" when we do so call it, or to 
cease to call it "this" on subsequent occasions when we have 
to mention it. In this respect, "this" differs from ordinary proper 

Equal difficulties arise if I say that "this" is a description. 

can of course mean **what I-now am noticing", but that only 
transfers the problem to "I-now". We have agreed to take "this" 
as our fundamental egocentric particular, and any other decision 
would have left us with precisely the same problem. No descrip- 



tion not involving some egocentric particular can have the peculiar 
property of "this", namely that it applies on each occasion of 
its use to only one thing, but to different things on different 


Exactly the same kind of objection applies to the attempt to 

as a general concept. If it is a general concept, it 



has instances, each of which is always an instance of it, and not 
only at one moment. There is obviously a general concept 
involved, namely "object of attention", but something more than 
this general concept is required in order to secure the temporary 
uniqueness of "this". 

It might be thought obvious that there would be no egocentric 
particulars in a purely physical world. This, however, is not an 
exact expression of what is true, partly because in a purely 
physical world there would be no words at all. What is true is 
that "this" depends upon the relation of the user of a word to 
the object with which the word is concerned. I do not want to 
bring in "mind". A machine could be constructed which would 
use the word "this" correctly: it could say "this is red", "this 

is blue", "this is a policeman", on suitable occasions. In the case 

of such a machine, the words "this is" are an otiose addition to 
the subsequent word or words; the machine might just as well 

abracadabra red", "abracadabra blue 

be constructed to say * 

and so on. If our machine, later on, said ''that was red", it would 

be getting nearer to the capacities of human speech. 

Let us suppose that our machine has this further capacity. We 
will suppose that red light, falling upon it, sets in operation a 
mechanism which causes it first to say 

this is red", and 



after various internal processes have been completed, "that was 
red". We can describe the circumstances under which the machine 



says "this" and those under which it says "that"; it says "this 
when the external cause first operates upon it, and it says "that 
when the first effect has led to certain further occurrences in the 

machine. I have seen automatic machines that played golf in 

return for a coin; the coin started a process which continued for 
a certain length of time. It would obviously be possible for the 


' ^ "-i . ' ^ 


process to begin by the machine saying "this is a penny*', and 

to end by its saying **that was a penny". I think the consideration 

of this ingenious toy may enable us to eliminate irrelevant 

What the machine does is to enable us to describe the cir- 
cumstances under which people say "this is" or "that was". A 
verbal reaction to a stimulus may be immediate or delayed. When 
it is immediate, the afferent current runs into the brain and con- 
tinues along an efferent nerve until it affects the appropriate 
muscles and produces a sentence beginning "this is". When it 
is delayed, the afferent impulse goes into some kind of reservoir, 
and only produces an efferent impulse in response to some new 
stimulus. The efferent impulse, in this case, is not exactly what 
it was in the previous case, and produces a slightly different 
sentence, namely one beginning "that was". 

We come-back here to minimal and other causal chains. 

minimal causal chain, in this connection, is the shortest possible 
chain from a stimulus outside the brain to a verbal response 
Other causal chains always involve some additional stimulus, 
causing the stored effect of the previous stimulus to be released 
and to produce a delayed verbal response. In the case of a minimal 
causal chain we say "this is", and in the case of a longer one we 
say "that was". This, of course, is too schematic to count 


actual physiology, but it seems sufficient to solve our difficulties 

of principle as regards egocentric particulars. 
Let us enlarge this statement. Whenever I utter the word "cat", 

do so— broadly speaking— because a cat is or was perceived 

T J ^^ ^^^ limitations to this statement may be ignored.) „ 
I do so because a cat was perceived, this past fact is obviously 
not the whole cause of my saying "cat"; there must also be some 

present stimulus. Thus the perceptive and the reminiscent uses 
of the word "cat" are not the results of precisely similar causes. In 
a person of suitably developed linguistic habits, the effects aUo 

are not precisely similar; the perceptive effect begins with the 

words this is , and the reminiscent effect with the words "that 




4fl 1 


the difference between a sentence beginning "this is" 

beginning "that was" lies not in their meaning, but in 
ea-usation. The two sentences "The Declaration of Inde- 
Pesmaence was in 1776", uttered by us, and "The Declaration of 
It\ciepen.<ience is in 1776", which might have been uttered 
*" have exactly the same meaning, but the former implies 

causation is indirect, and the latter that it is direct, or 

as possible. 

It might be objected that many statements about the present 
cjuitze as indirect as statements about the past. If I say "Finland 

invaded", I do so because, first, I remember what I 

ad in the newspaper, and secondly, I infer that the in- 

is not likely to have ceased in the last few hours. But this 

deirivative and inferential use of "is", involving causal laws 

l>y wfciioh knowledge of the present is obtained from knowledge 

past. The "present" that is involved is not the "present" 
jysychobgkal sense; it is not something "presented". It 
^ ^present" in the physical sense, i.e., something which, in 

time, is contemporaneous with the psychological 

. "Present" and "past" are primarily psychological 

in the sense of involving diifferent causal relations between 

and that of which he speaks; their odier uses are 
defitiLable in terms of this primary use. 

the above theory explain the use of the word "I" ? We 

the beginning of this chapter that "I" could be defined 

of "this": "I" is the biography to which "this" belongs, 
although we have explained the use of the word "this", we 
clone so by depriving the word itself of all significance in 
isolation. We cannot therefore be sure that the above definition 


can be maintained. 
if our theory of "this" is correct, it is a word which is not 

for a complete description of the world* We wish to 


that the same conclusion holds as regards "I" and other 

egoootitric words 

word "I", since it applies to something which persists 

tliroxighout a certain period of time, is to be derived from 








now'*, as 

that series of events which is related to 



certain causal relations. The phrase to be considered is 




which may be replaced by "I-now is", where the "is" may be 

regarded as timeless. 
The connection between **I-now" 



' is obviously 
very close. "I-now" denotes a set of occurrences, namely all those 

that are happening to me at the moment 



one of these 

occurrences. "1", as 

Opposed to 


denotes some 

\ can be 




defined by causal relations to "this", just as well as to "I-now 
for I can only denote by "this" something that I am experiencing. 
For reasons which will appear more fully in later chapters, I 
think that the phrase "I am" can always be replaced by the phrase 
"this is", or vice versa. Which of the two phrases we use depends 
upon accident or prejudice. We say "I am hot" rather than "this 
is hotness", if we are hot from exercise and not because of the 
surrounding temperature. But when we go into the engine-room 

a ship, we say 


(roughly) to "this is hotness 

Ouf ! it is hot here", which is equivalent 




is a cat", and 

intend to make a statement about something which is not merely 
a part of our own biography. But if the word "this" is to apply 
as it should, to something that we directly experience, it cannot 
apply to the cat as an object in the outer world, but only to our 
own percept of a cat. Thus we must not say "this is a cat", but 

this is a percept such as we associate with 

cats", or 


IS a 

cat-percept". This phrase, in turn, can be replaced by "I am 



asserts a state of myself, and is true on 

cat-perceptive , 

exactly the same occasions as those on which 


am tempted 

(rashly) to say * 

saying "this is a cat-percept". What we directly know when we 

IS a cat ', and on which I am justified in 

say "this is a cat" is a state of ourselve 

like being hot 

^^ Thus in every statement containing "this" we may substitute 
"what I-now notice", and in every statement containing '1-now" 
we may substitute "what is compresent with this*' 

follows that what has been said of "this" i 






what distinguishes "L " 

is no part of what is stated 

applies equally 
a proper name 
a sentence containing "I-now", 




I 1 



but is only an expression of the causal relation between what 
is stated and the stating of it. 

The word "you" involves difficulties other than those charac- 
teristic of egocentric particulars; these difficulties will be con- 
sidered in later chapters. So far as our present problem is con- 
cerned, it is sufficient to notice that "you'* is always determined 
by relation to some present percept, which at the moment is 


this*'. Consequently the explanation of 



also explains 






in so far as the difficulty is that of egocentric particulars. 

can see, solves the problem of egocentric 


far as 

particulars, and shows that they are not needed in any part of 
the description of the world, whether physical or psychological. 


Professor Reichenbach has kindly allowed me to 

see an unpublished treatment by him of the question of 
"egocentric particulars". He approaches the problem in 
a somewhat different way, but I do not think there is any 
inconsistency betv^^een his theory and mine, which complete 
each other. 






Chapter VIII 


The word "perception" is one which philosophers, at an early 
stage, took over, somewhat uncritically, from common sense. 
Tlieaetetus, when Socrates asks him for a definition of "know- 
ledge", suggests that knowledge is perception. Socrates persuades 
him to abandon this definition, mainly on the ground that per- 
cepts are transient, whereas true knowledge must be of something 
eternal ; but he does not question the occurrence of perception 
conceived as a relation between subject and object. To common 
sense it seems obvious that we perceive "things", at any rate 
with the senses of sight and touch. Sight may, on occasion, be 
misleading, as in the case of Macbeth's dagger, but touch never. 
An "object" is etjmiologically something thrown up in my way: 

if I run into a post in the dark, I am persuaded that I perceive 
an "object", and do not merely have a self-centred experience 
This is the view implied in Dr. Johnson^s refutation of Berkeley. 

From various points of view, this common sense theory of 
perception has been called in question. The Cartesians denied 
interaction between mind and matter, and could not therefore 
admit that, when my body runs into a post, this event is the 
cause of the mental occurrence which we call "perceiving the 
post". From such a theory it was natural to pass either to psycho- 
physical parallelism, or to Malebranche*s doctrine that we see all 
things in God, or to Leibniz's monads which all suffer simul- 
taneous similar but systematically differing illusions called "mir- 
roring the universe". In all these systems, however, there was 
felt to be something fantastic, and only philosophers with a long 
training in absurdity could succeed in believing them. 

A much more serious attack on the common sense theory of 



quanta, which travel across the space between the sun and my 
eye in the course of about eight minutes. When they reach my 
eye, their energy is transformed into new kinds : things happen 
in the rods and cones, then a disturbance travels along the optic 
nerve, and then something (no one knows what) happens in the 
appropriate part of the brain, and then I "see the sun". This is 
an account of the causal relation between the sun and ^'seeing 

the sun". But what we want to know is the resemblance^ if any, 

between the sun and "seeing the sun"; for it is only in so far 
as there is resemblance that the latter can be a source of know- 
ledge concerning the former. 

Adhering to our uncritical acceptance of science, we find that 
there are important resemblances between the sun and "seeing 
the sun". To begin with, the sun looks round and is round. This 
resemblance, it is true, is not so close as it sounds, for the sun 
looks round in my visual space and is round in physical space. 
Nevertheless, the resemblance can be clearly stated. The defi- 
nition of roundness is the same in one space as in another, and 

certain relations — notably contiguity — ^are common to physical 

and visual space. 

Again: if we see sun-spots, there are sun-spots. In the sense 
just explained, the spots in the astronomical sun have the same 
shape (roughly speaking) as the spots in the visual sun. More- 
over the sun feels hot, and the astronomical sun has a correspond- 
ing property sis contrasted with the surrounding regions of 


There are, however, limitations to the similarities of the visual 

, »^TT^*X,«, 

and ^astronomical sun. During a partial eclipse, the sun looks like 
the c^cent moon, but is just as round as at other times. By 
squinting we can see two suns, but cannot create two "real" 
suns. All such matters, however, can be dealt with in detail, and 
raise no difficulty of principle. 

began widi astronomical objects, because of the simplicity 
derived from their being perceptible to only one sense. Let us 
now consider ordinary terrestrial objects. Berkeley considers a 
tree, and this will do as well as any other. So far as the sense 





I ^ 

of sight 


peB-CEPTion and knowledge 

concerned, everything that has just been said about 
the sun applies eq^^iUy to the tree, except that the light by which 
we see it is reflected light, so that it is invisible except when it is 
exposed to light from the sun, or to lightning, or to some arti- 
ficial illumination- But the tree can also be touched, heard, smelt, 

"touch" the tree, certain electrons in my 

and tasted 


finger are sufficiently near to certain electrons in the tree for 
violent forces of repulsion to be generated; these cause a dis- 
turbance to travel along the nerves from my finger to the brain 

where they 
causes a 


an effect of unknown nature, which finally 
of touch. Here, again, we have to ask our- 
selves: what resemblances are there between my sensation of 

touch and the *part of the tree with which I falsely imagine my 

finger to be in contact ? 

There are qualities of touch — hard and soft, rough and smooth 
which correspond to qualities of the object touched. By feeling 

round an object, we can infer its shape, just as we can by seeing 


shape inferred is the same for a man who sees the 
object and for a blind man who only feels it. And when I say 

it: the 




mean strictly the same 

ere is no difference 

between the physical space inferred from touch and that from 
sight, except as regards degrees of nicety. 

In addition to shape, there is location. An object touched but 

above my head or at my feet or at any inter- 

not seen may 

mediate altitude; it may 

face, or in 
body. In 


be at arm's length, or touching my 
of a multitude of positions relative to my 

these respects 


there is a similarity between my 

sensations and the properties of the physical object 



consider hearing, smell, and taste, smce 

exactly similar considerations apply. 

The above account rests upon a dogmatic acceptan 


physics and physiology. Before 


relinquish this comfortable 


are some points to be added. The sensations 

caused by external objects are events like any others, and have 
not the characteristics that we associate with the word 


• . • 




fact has to be brought into relation with the 


J 1 


common-sense view that there are occurrences called perceivings, 
in which we become aware of objects. Shall we completely aban- 
don this common-sense view, or shall we retain it, by making 
the perceptual object something quite different (except /or the 
above-noted resemblances) from the physical object ? And before 
dealing with this question we must examine the psychological 

distinction between 











here, being still merely a certain kind of event resulting 

from a stimulus, and not being assumed to have any cognitive 

In our reaction to a sensory stimulus there are two theoreti 
cally distinguishable elements, first, that due merely to the stimu 

that due to its habitual concomitants. A visual sen 
sation is never pure: other senses are also stimulated in virtue 
of the law of habit. When we see a cat, we expect it to mew, to 
feel soft, and to move in a cat-like manner; if it barked, or felt 
like a stone, or moved like a bear, we should experience a violent 
shock of surprise. This sort of thing has to do with our belief 

lus, second 


that we see 





and do not merely have visual sensations 

If we are considering the psychology of animals, and not only 
of human beings, it is not safe to attribute this filling-out entirely 
to habit; some of it seems to be of the nature of innate refliex. 
This is shown, for example, in a chicken's power of pecking at 
grains, without first having to learn a "beak-eye'' coordination. 
The question of habit versus unconditioned reflex is, however, 
in this connection, not very important; what is important is that 
sensations are rounded out by spontaneous images or expectations 
of their usual accompaniments. 

When we have the experience which we call .^ ^ 

there is an antecedent causal chain analogous to that which we 

When the expe 

"seeing a cat" 


considered in connection with "seeing the sun" 

rience is veridical, this causal chain, at a certain point in its bade 

am still dogmatically assuming 

ward course, reaches a cat 

the truth of physics.) But it is clear that if, at any point in this 
chain, the event (light-waves 

,. 1 r v-es-w »Y«vto, agitauun ui roQs ana cones, or 

disturbance of optic nerve or brain) which usually has its origin 

1 20 

K ^ 




tn. a cat 

can be produced otherwise, we shall have exactly the 

, without any cat being there. 


"seeing a cat" 

must beg the reader to remember that I am talking science, not 
philosophy. I am thinking of such things as images in mirrors, 

of a blow on the eyes in causing a man to see stars, 
erebral disturbances (whatever they are) which may cause 



see a cat 


in a dream 

^e may put the matter schematically as follows 


experience E (e.g 

that which is the visual core in what we call 
a cat") has, in my previous history, been usually closely 
accompaiued by certain other experiences. Hence, by virtue of the 
larw of habit, the experience E is now accompanied by what Hume 
^would call * 


\ but what I should prefer to call "expecta 
which may be purely bodily states. In any case, these 

pectations deserve to be called "beliefs", as we shall find later 

-we come to analyse belief. Thus while the sensory core 
not cognitive, its associative accompaniments, being beliefs 


be classed as cognitions (including possibly erroneous 
under this head). If this view seems odd, that is because 
tend to think of beliefs in an unduly intellectualist fashion. 

do not like to use the word "perception" for the complete 
csxperience consisting of a sensory core supplemented by expec- 

suggests too strongly 

because the word 


the beliefs involved are true. I will therefore use the phrase 

perceptive experience 


Thus whenever I think I see a cat. 

have the perceptive experience of "seeing a cat 
occasion, no physical cat is present. 


even if, on this 

the filling out of the sensation mto a perceptive expe 


rience is an example of habit, it follows that, in my past 
collocations which the perceptive experience assumes have usually 
existed. Put briefly — ^and still assuming physics — ^hitherto, when 


"seen a cat" 

there has usually been a cat to be seen, 
for if this had not beein the case I should not have acquired the 
habits which I now have. We have therefore inductive grounds 
for holding (on a common sense basis) that when I 

"see a cat" 

probably is a cat. We cannot go beyond, "probably". 







■ ' -~r-ii-- 



I *, 



:%^ .-.'f i 









. V-'. 



i^ ■■ 




















we know that people sometimes see cats that are not there, for 
instance in dreams. And the possibility of perceptive experiences 
as results of sensory stimuli depends entirely upon the fact that 
we live in a world in which objects have a certain stability and 
also fit into natural kinds. These things depend upon temperature. 
So, no doubt, does the possibility of life. Certainly "experience" 
depends upon our having a more or less stable body, 
in the etymological sense — ^i.e., a gas in motion — ^would not have 

the physical stability required for experience or the formation 
of habits. 

To sum up this part of our discussion : in our environment 
it frequently happens that events occur together in bundles 
such bundles as distinguish a cat from another kind of object. 
Any one of our senses may be affected by a stimulus arising from 
some characteristic of the bundle in question. Let us suppose the 
stimulus to be visual. Then physics allows us to infer that light 
of certain frequencies is proceeding from the object to our eyes. 
Induction allows us to infer that this pattern of light, which, 
we will suppose, looks like a cat, probably proceeds from a region 
in which the other properties of cats are also present. Up to a 
point, we can test this hypothesis by experiment: we can touch 
the cat, and pick it up by the tail to see if it mews. Usually the 
experiment succeeds; when it does not, its failure is easily 
accounted for without modifying the laws of physics. (It is in 
this respect that physics is superior to ignorant common sense.) 
But all this elaborate work of induction, in so far as it belongs 
to common sense rather than science, is performed spontaneously 
by habit, which transforms the mere sensation into a perceptive 
experience. Broadly speaking, a perceptive experience is a dog- 
matic belief in what physics and induction show to be probable 
it is wrong in its dogmatism, but usually right in its content, 

in any perceptive experience 


results from the above that 

the sensory core has higher inferential value than the rest. I may 
see a cat, or hear it mew, or feel its fur in the dark. In all these 

a perceptive experience of a cat, but the first is a 
visual experience, the second auditory, the third tactile. In order 

cases, I have 



•i I 


to infer from my visual experience the light-frequencies at the 
surface of the cat, I need (if I am not dreaming and my eyesight 
is normal) only the laws of physics; but in order to infer the 
other characteristics of cats, I need, further, the experience that 
objects having such coloured shapes are more apt to mew than 
to bark. While, therefore, none of the inferences from the 
ceptive experience is certain, the inferences drawn from the sen 
sory core have a higher probability than those drawn from the 
other parts of the perceptive experience. This can only be denied 
by those who are willing to deny physics or physiology. 

now pass to a slightly different topic, namely, the relation 


of perceptive experiences to our knowledge of matters of fact. 
That there is such a relation is evident from the difference between 
our knowledge of the experienced past and present on the one 
hand, and our knowledge of the future and the unexperienced 
past and present on the other hand. We know that Caesar was 
murdered, but until this event occurred it was not known. 

was known to eye-witnesses because they perceived it; it is known 
to us because of statements that we perceive in history-books. 
We sometimes know future facts, for instance the dates of coming 
eclipses ; but such knowledge is inferred inductively from know- 
ledge based directly on percepts, and is less certain than the 
knowledge upon which it is based. All our knowledge of matters 
of fact — i.e., all knowledge in which there is a reference to 
temporal position — is causally dependent upon perceptive expe- 
riences, and involves at least one premiss referring to the present 
or the past. But while this is obvious, the logical relation of 
empirical knowledge to perceptive experience is by no means 

easy to state clearly. 

There are some schools of philosophy— notably the Hegelians 
and the instrumentalists — ^which deny the distinction between 



data and inferences altogether. They maintain that in 
knowledge there is an inferential element, that knowledge is an 
organic whole, and that the test of truth is coherence rather than 

conformity with "fact". I do not deny an element of truth in 
this view, but I think that, if taken as the whole truth, it renders 



1 * 


the part played by perception in knowledge inexplicable. It is 
surely obvious that every perceptive experience, if I choose to 


notice it, affords me either new knowledge which I could not 
previously have inferred, or, at least, as in the case of eclipses, 
greater certainty than I could have previously obtained by means 
of inference. To this the instrumentalist replies that any state- 
ment of the new knowledge obtained from perception is always 
an interpretation based upon accepted theories, and may need 
subsequent correction if these theories turn out to be unsuitable. 
If I say, for example, "Look, there is an eclipse of the moon", 
I use my knowledge of astronomy to interpret what I see. No 
words exist, according to the instrumentalist, which do not 
embody theories or hypotheses, and the crude fact of perception 
is therefore for ever ineffable. 

think that this view underestimates the powers of analysis. 
It is undeniable that our every-day interpretations of perceptive 
experiences, and even all our every-day words, embody theories. 
But it is not impossible to whittle away the element of inter- 
pretation, or to invent an artificial language involving a minimum 

of theory. By these methods we can approach asymptotically to 
the pure datum. That there must be a pure datum is, I think, 
a logically irrefutable consequence of the fact that perception 
gives rise to new knowledge. Suppose, for example, that I have 
hitherto entertained a certain group of theories, but I now per- 
ceive that somewhere among these theories there is a mistake. 
There is necessarily, in this case, something not deducible from 
previous theories, and this something is a new datum for my 
knowledge of matters of fact, for we mean by a "datum'* merely 
a piece of knowledge that is not deduced. To deny data in this 
sense is, it seems to me, only possible for a Hegelian panlogism. 
The question of data has been, mistakenly as I think, mixed 

up witli the question of certainty. The essential characteristic 
of a datum is that it is not inferred. It may not be true, and we 
may not feel certain diat it is true. The most obvious example 
is memory. We know that memory is fallible, but there are many 
things that we beKeve, though not with complete assurance 

, on 




the basis of memory alone. Another example is derived from 
faint perceptions. Suppose you are listening to a sound which 
is gradually growing more distant, for example, a receding aero- 
plane. At one time, you are sure that you hear it ; at a later time, 
you are sure that you do not hear it. At certain intermediate 

still hear it, but cannot 


sure: at 

times, you think that you 

these times you have an uncertain datum. I am prepared to 

concede that all data have some uncertainty, and should there- 

fore, if possible, be confirmed by other data. But unless these 
other data had some degree of independent credibility, they would 
not confirm the original data. 

There is here, however, a distinction to be made. While I 
hold that no actual statement in words is completely indubitable, 
it is possible to define classes of statements which are certainly 
all true; in this case, what is doubtful is whether a given state- 
ment belongs to one of these classes. For many purposes, it is 
convenient to define the class of premisses so that all are true ; 
but if we do so, we can never be sure that a given statement 
belongs to the class of premisses. 

shall henceforth assume that there are data, in the sense of 
propositions for which the evidence is not wholly derived from 
their logical relation to other propositions. I shall not assume 
that the actual data which we can obtain are ever completely 
certain, nor yet that a proposition which is a datum cannot be 
also a consequence of other accepted propositions. This latter 
case occurs whenever we see a predicted eclipse. But when a 
proposition concerning a particular matter of fact is inferred, 
there must always be among the premisses odier matters of^fact 
from which some general law is obtained by induction. " 
therefore impossible that all our knowledge of matters of fact 

should be inferred. 

The question of how to obtain from perceptual experiences 
propositions which are premisses for empirical knowledge is 
difficult and complicated, but fundamental for any empincal 

theory of knowledge. 

We must now examine a question of considerable importance, 





namely, that of the part played by egocentric particulars in per- 
ceptive judgments. We may first set out the nature of the prob- 
lem, which is as follows. We saw in Chapter VII that it is the ideal 
of science to dispense with egocentric particulars, and it seemed 
from the discussion in that chapter, as if this ideal were attainable. 
If it is attainable, there can be empirical impersonal knowledge 
and two men who both believe (say) that hydrogen is the lightest 
of elements may be both believing the same proposition. If, on 
the other hand, all empirical words are, strictly speaking, defined 
in terms of egocentric particulars, then, since two people cannot 
attach the same meaning to the same egocentric words, no two 
people can attach the same meaning to any empirical word, and 
there is, no empirical proposition that two different people can 
both believe. This unpleasant conclusion has, however, much 
to be said in its support. Our empirical vocabulary is based upon 
words having ostensive definitions, and an ostensive definition 
consists of a series of percepts which generate a habit. When 
the vocabulary has been mastered, it is perception that gives us 
the primary knowledge of matters of fact upon which science 
is based; and perceptive knowledge, jorima ^cfe, demands ego- 
centric words in its verbal expression. This argument must now 

be scrutinized. 

Let us begin with "meaning", and let us take the word "hot" 
for purposes of illustration. I shall suppose a schematic simplicity 

in the experiences by means of which I learnt the meaning of 

the word in childhood : that there was an open fire in my nursery, 

and every time I went near it someone said "hot"; that they used 

the same word when I perspired on a summer's day, and when 


that I uttered the word 

spilled scalding tea over myself. The result was 




whenever I noticed sensations of 

a certain kind. So far, we have nothing beyond a causal law 
a certain kind of bodily state causes a certain kind of noise 

^ hot 
whenever it reached a certain temperature. This, however, is not 

would be easy to construct a machine which would say 

for us, the important point. What is important 
this primitive use of the word * 




has the distinctive charac- 


for us, is 







teristic of egocentric particulars, namely (to quote Chapter VII) 
that it "depends upon the relation of the user of the word to 
the object with which the word is concerned". We have held 
throughout our discussion of object-words, that, in their most 
primitive use, they are perceptive judgments: what we express 
at first by the one word "hot!" is what we afterwards express 
by "this is hot" or "I am hot"* That is to say, every object-word 
in its primitive use, has an implicit egocentricity, which the sub- 
sequent development of speech renders explicit. 

But when we have advanced to the point at which we can 
explicitly consider the meanings of words, we see that this 
egocentricity is no part of the meaning of the word "hot" as 
it exists in a developed language. The word "hot" means only 
that quality in occurrences which, if the occurrences are suitably 
related to me, will make them causes of my utterance of the word 
"hot". In passing from "hot!" to "this is hot", we effect an 
analysis: the quality "hot" is freed from egocentricity, and the 
formerly implicit egocentric element is rendered explicit by the 
words "this is". Thus in a developed language object-words 
such as "hot", "red", "smooth", etc., are not egocentric. 

This, however, does not decide as to the egocentric element 
in judgments of perception. The question is^: can we express what 
we know when we make such judgments, without the use of 
"this" or "I-now"? If we cannot, the theory of proper names 
suggested in Chapter VI will have to be abandoned. 

Perceptive judgments, on the face of it, are of two kinds. 
In looking at a fire we may say "this is hot" and "this is bright"; 
these are of the first kind. But we may also say "hotness and 
brightness are compresent"; this is of the second kind. When- 
ever we can say "this is A, this is B, this is C, etc.", where "A" 
"B", "C", • . , are names of qualities, we can also say "A, B 
, . . are compresent". But in this latter judgment the spatio- 
temporal uniqueness of "this" is lost; we are no longer speaking 
of this occasion, and, so far as our judgment shows, there may 
be many occasions on which A, B, C, . • • are all compresent. 

If we are to preserve the theory of Chapter VI, we shall have 



? ^> 





to say that "this" is a name (with the limitations explained in 

Chapter VII) of a bundle of compresent qualities, and that, 
our qualities are suitably chosen or sufficiently numerous, the 
whole bundle will not occur more than once, i.e., will not have 

to itself any of those spatial or temporal relations which we 
regard as implying diversity, such as before, above, to the right 
of, etc* If this theory can be maintained, the egocentricity in such 
a proposition as "this is hot" lies, not in what is known, but 
in the causation of our knowledge and in the words by means 
of which we express it. The word "this" may be replaced by 
something that is strictly a name, say "W", denoting that whole 
complex of qualities which constitutes all that I am now expe- 
riencing. The impersonal truth asserted when I say "this is hot" 
will then be translated into the words "hotness is part of W". 
In this form, what I have learnt from perception is ready for 
incorporation in impersonal science. 

Whether we accept or reject this view, grave difHculties con- 
front us. Let us examine first those involved in acceptance. 

There are, to begin with, certain difficulties as to space-time. 

These were considered in Chapter VI, and I shall assume that 
they were there satisfactorily disposed of. 

More serious is the apparent consequence that all judgments 

of perception are analytic. If "W" is the name of a whole con 
sisting of a bundle of qualities, and " this is hot" only says diat 
hotness is one of the qualities composing W, then, as soon as 
"W" is defined, the proposition "this is hot" becomes analogous 
to such propositions as "rational animals are animals" or "hexa- 
gons are polygons". But this is absurd: it does away with the 
distinction between empirical and logical knowledge, and makes 
the part played by experience in empirical knowledge inexplicable. 
The only answer is to say that, although "W" is, in fact, the 
name of a certain bundle of qualities, we do not know, when 
we give the name, wAat qualities constitute W. That is to say 
we must suppose that we can perceive, name, and recognize a 
whole without knowing what are its constituents. In that case 
the datum which appears as subject in a judgment of perception 





is a complex whole, of which we do not necessarily perceive 
the complexity. A judgment of perception is always a judgment 
of analysis, but not an analytic judgment. It says "the whole W, 
and the quality Q, are related as whole-and-part**, where W and Q 
are independently given. The fact that they are "given'* enters 
into the causation of what we know, and into its verbal expression 
if we use the word **this**, but not into its verbal expression 

in the form "Q is part of W". 

The above theory has the consequence that we caimot express 
our knowledge without names for complex wholes, and that we 
can be acquainted with complex wholes without knowing of what 
constituents they consist. I shall revert to this question in Chap- 
ter XXIV, where grounds will be given for accepting the view 
as to wholes that our present theory requires. 

I conclude, provisionally, that the difficulties of accepting our 
present theory are not insuperable. 

Let us now examine the difficulties which result from reject- 
ing it. 

If we reject our theory, we accept either "diis" or "I-now 

as a necessary constituent of judgments of perception. I shall 
assume that we adhere to "this". The argument is exactly the 
same whichever alternative we choose 

The difficulty that arises here is not as to egocentric particulars, 

but as to "substance". If I admit propositions of the form "this 

hot" where "this" does not designate a bundle of qualities 

then "this" becomes the name of something which is merely a 
sub j ect of predicates, and which serves no purpose except that 
predicates "inhere" in it. All propositions of the form "this is 
hot" are supposed to be synthetic, so that "this" is not defined 
when aU its predicates are enumerated. If it were, it would be 
superfluous, and we could revert to the theory that "this 
denotes a bundle of qualities (which now are no longer syn- 
tactically predicates). We must therefore hold it possible t|at 
this and that should have exactly the same predicates, f he 
identity of indiscemibles, if true, wUl be a fortunate acxident, 
and "identity" wiU be an indefinable. Moreover it may happen 




that this and that are not identical, although no evidence of this 

is imaginable. Counting will be impossible, for, if a and b are 

indistinguishable, I shall give them the same name, and any act 

in which I count one of them will necessarily be also an act in 
which I count the other. It is clear therefore that, if there be a 
concept of identity which allows indiscernibles to be not iden- 
tical, such a concept can never be applied, and can have no 
relation to our knowledge. We should, therefore, prefer a theory 
which does not require it. 

conclude, therefore, that the theory of proper names de- 
veloped in Chapter VI is to be maintained, and that all knowledge 
stated by means of egocentric particulars can be stated without 
emplojdng them. 

Chapter IX 


Theory of knowledge is rendered difficult by the fact that it 


nvolves psychology, logic, and the physical sciences, with the 


esult that confusions between different points of view are 
constant danger. This danger is particularly acute 



with the problem of our present chapter, which is that of deter- 
mining the premisses of our knowledge from an epistemological 
point of view. And there is a further source of confusion in the 
fact that, as already noted, theory of knowledge itself may be 
conceived in two different ways. On the one hand, accepting 
as knowledge whatever science recognizes as such, w^e may ask: 
how have we acquired this knowledge, and how best can we 
analyse it into premisses and inferences ? On the other hand, we 
may adopt the Cartesian standpoint, and seek to divide what 

passes for knowledge into more certain and less certain portions. 
These two inquiries are not so distinct as they might seem, for, 
since the forms of inference involved are not demonstrative, our 
premisses will have more certainty than our conclusions. But 
this fact only makes it the more difficult to avoid confusion 
between the two inquiries. 

An epistemological premiss, which we shall now seek to define, 
must have three characteristics. It must be (a) a logical premiss, 
{i) a psychological premiss, and (c) true so far as we can ascertain. 

Concerning each of these something .must be said. 

(a) Given any systematic body of propositions, such as is 
contained in some science in which there are general laws, it is 
possible, usually in an indefinite number of ways, to pick out 
certain of the propositions as premisses, and deduce the re- 
mainder. In the Newtonian theory of the solar system, for 



example, we can take as premisses the law of gravitation together 
with the positions and velocities of the planets at a given moment. 
Any moment will do, and for the law of gravitation we can 
sxibstitute Kepler's three laws. In conducting such analyses, the 
logician, as such, is indifferent to the truth or falsehood of the 
body of propositions concerned, provided they are mutually 
consistent (if they are not, he will have nothing to do with them). 
He will, for example, just as willingly consider an imaginary 
planetary system and a gravitational law other than that of the 
inverse square. Nor does he pretend that his premisses give the 
grounds for believing in their consequences, even when both 
are true. When we are considering grounds of belief, the law 
of gravitation is an inference, not a premiss 

The logician, in his search for premisses, has one purpose 
which is emphatically not shared by the epistemologist, namely, 
that he seeks a minimum set of premisses. A set of premisses is 
a minimum set, in relation to a given body of propositions, if 
from the whole set, but not from any part of the set, all the given 
body of propositions can be deduced. Usually many minimum 
sets exist; the logician prefers those that are shortest, and, among 
two equally short, the one that is simplest. But these preferences 
are merely aesthetic. 

(b) A psychological premiss may be deiined as a belief which 
is not caused by any other belief or beliefs. Psychologically, any 
belief may be considered to be inferred when it is caused 
other beliefs, however invalid the inference may be for logic. The 
most obvious class of beliefs not caused by other beliefs are those 
that result directly from perception. These, however, are not the 
only beliefs that are psychological premisses. Others are required 
to produce our faith in deductive arguments. Perhaps induction 
also is based, psychologically, upon primitive beliefs. What others 
there may be I shall not at the moment inquire. 

Since we are concerned with theory of knowledge^ not 
merely of beliefs we cannot accept all psychological premisses 
as epistemological premisses, for two psychological premisses 
may contradict each other, and therefore not all are true. For 



example I may think "there is a man coming downstairs", and 

the next moment I may realize that it is a reflection of myself 

in a mirror. For such reasons, psychological premisses must be 
subjected to analysis before being accepted as premisses for theory 
of knowledge- I^^ diis analysis we are as little sceptical as possible. 
We assume that perception ccai cause knowledge, although it 
may cause error if we are logically careless. Without this fund- 
amental assumption, we should be reduced to complete scep- 
ticism as regards the empirical world. No arguments are logicaUy 

possible either for or against complete scepticism, which must 
be admitted to be one among possible philosophies. It is, how 

ever, too short and simple to be interesting. I shall, therefore, 
without more ado, develop the opposite hypothesis, according 
to which beliefs caused by perception are to be accepted unless 
there are positive grounds for rejecting them. 

Since ^we can never be completely certain that any given pro- 
position is true, we can never be completely certain that it is 
an epistemological premiss, even when it possesses the other two 
defining properties and seems to us to be true. "We shall attach 
different **-weights" (to use a term employed by Professor 

Rdchenbach) to different propositions which we believe and 
which, if true, are epistemological premisses : the greatest weight 
will be ffiven to those of which we are most certain, and the 

least to 


of which we are least certain. Where there is a 
we shall sacrifice the less certain, unless a large 
number of these are opposed to a very small number of the 

more certain. 

O^ving to the absence of certainty, we shall not seek, like the 
logician, to reduce our premisses to a minimum. On the contrary, 
we shall be glad when a number of propositions which support 

since this increases the probability of all of them. (I am not 
thinking of logical deducibility, but of inductive compati- 


Epistemological premisses are different according as they are 
momentary, individual, or social. Let us illustrate. I believe diat 


one another can all be accq)ted as epistemological premisses 


1 62 = 256; at the moment, I believe this on grounds of memory, 
but probably at some time I did the sum, and I have convinced 
myself that the received rules of multiplication follow from the 
premisses of logic. Therefore taking my life as a whole, 16^ == 256 
is inferred, not from memory, but from logic. In this case, if my 
logic is correct, there is no difference between the individual and 

the social premisses. 

But now let us take the existence of the Straits of Magellan, 
Again, my momentary epistemological premiss is memory. But 

have had, at various times, better reasons: maps, books of 

travel, etc. My reasons have been the assertions of others, whom 
believed to be well-informed and honest. Their reasons, traced 

back, lead to percepts: Magellan, and others who have been in 
the region concerned when it was not foggy, saw what they 
took to be land and sea, and by dint of systematized inferences 
made maps. Treating the knowledge of mankind as one whole, 
it is the percepts of Magellan and other travellers that provide 
the epistemological premisses for belief in the Straits of Magellan. 
Writers who are interested in knowledge as a social phenomenon 
are apt to concentrate upon social epistemological premisses. For 
certain purposes this is legitimate, for others not. Social epis- 
temological premisses are relevant in deciding whether to 
spend public money on a new telescope or an investigation of 
the Trobriand Islanders. Laboratory experiments aim at estab- 
lishing new factual premisses which can be incorporated in the 
accepted system of human knowledge. But for the philosopher 

there are two prior questions: what reason (if any) have I for 
believing in the existence of other people.'* And what reason 

(if any) have I now for believing that I existed at certain past 

times, or, more generally, that my present beliefs concerning 
past times are more or less correct? For me now^ only my moment- 
ary epistemological premisses are really premisses; the rest must 
be in some sense inferred. For me as opposed to others, my 
individual premisses are premisses, but the percepts of others 
are not. Only those who regard mankind as in some mystical 
sense a single entity possessed of a single persistent mind have 



a right to confine their epistemology to the consideration of 
social epistemological premisses. 

In the light of these distinctions, let us consider possible defi- 
nitions of empiricism. I think that the great majority of empiricists 
are social empiricists, a few are individual empiricists, and hardly 
any are momentary empiricists. What all empiricists have 
common is emphasis upon perceptive premisses. We shall seek 
a definition of this term presently; for 
only a few preliminary words. 


e moment 





Speaking psychologically, a "perceptive premiss" may be 
defined as a belief caused, as immediately as possible, by a per- 
cept. If I believe there will be an eclipse because the astronomers 
say so, my belief is not a perceptive premiss; if I believe there 

is an eclipse because I see it, that is a perceptive premiss. But 
immediately difficulties arise. What astronomers call an eclipse 

IS a 




whereas what 

am seeing may be due to a 


defect in my eye or my telescope. While, therefore, the belief 
"there is an eclipse" may arise in me without conscious inference 
this belief goes beyond the mere expression of what I see. Thus 
we are driven, in epistemology, to define "perceptive premiss" 
more narrowly than would be necessary in psychology. We are 

driven to this because we want a 


perceptive premiss 


to be 

something which there is never good reason to think false, or, 
what comes to the same thing, something so defined that two 
perceptive premisses cannot contradict each other. 
Assuming "perceptive premisses" to have been adequately 



let us return to the definition of 




momentary knowledge consists largely of memory 
individual knowledge consists largely of testimony. But memory, 
when it is veridical, is related to a previous perceptive premiss, 
and testimony, when it is veridical, is related to some one else*s 


perceptive premiss. Social empiricism takes these perceptive 
premisses of other times or other persons as the empirical pre 
misses for what is now accepted, and thus evades the problems 
connected with memory and testimony. This is plainly illegiti- 
mate, since there is reason to believe that both memory and 




testimony sometimes deceive. I, now, can only arrive at the 

perceptive premisses of other times and other persons by an 

inference from memory and testimony. If I, now, am to have 
any reason to believe what I read yesterday in the Encyclopaedia, 

must, now, find reason to trust my memory, and to believe 
in suitable circumstances, what comes to me in the form of tes- 


timony. I must, that is to say, start from momentary epistemo- 
logical premisses. To do anything else is to evade problems which 
it is part of the business of epistemology to consider. 

follows from the above considerations that epistemology 
cannot say: "knowledge is wholly derivable from perceptive 
premisses together with the principles of demonstrative and 
probable inference". Memory premisses, at least, must be added 
to perceptive premisses. What premisses, if any, must be added 
in order to make testimony admissible (with common sense 
limitations), is a difficult question, which must be borne in mind, 
but need not be discussed at the moment. The paramount im- 
portance of perception, in any tenable form of empiricism, is 
causal. Memory, when veridical, is causally dependent upon a 
previous perception; testimony, when veridical, is causally depen- 
dent upon some one else's perception. We may say, therefore: 
"all human knowledge of matters of fact is in part caused by 
perception". But a principle of this sort is clearly one which can 
only be known by inference, if at all; it cannot be a premiss 

in epistemology. It is fairly clear that part of the cause of my 
believing in the Straits of Magellan is that certain people have 
seen them, but this is not the ground of my belief, since it has 
to be proved to me (or rather made probable) that such people 
have had such percepts. To me, their percepts are inferences, 
not premisses 




*'Basic Propositions**, as I wish to use the term, are a sub 
class of epistemological premisses, namely those which are caused 

as immediately as possible, by perceptive experiences. This 
excludes the premisses required for inference, whether demon- 
strative or probable. It excludes also any extra-logical premisses 
used for inference, if there be such — e.g., "what is red is not 

blue", "if A is earlier than B, B is not earlier than A". Such 

propositions demand careful discussion, but whether premisses 
or not, they are in any case not "basic" in the above 

I have borrowed the term "basic proposition" from Mr. A. J. 
Ayer, who uses it as the equivalent of die German ProtokoUsati 

employed by the logical positivists. I shall use it, perhaps, not 
in exactly the same sense in which it is used by Mr. Ayer, but 
shall use it in connection with the same problems as those 
which have led him and the logical positivists to require such 
a term. 

Many writers on theory of knowledge hold that from a single 
occurrence nothing is to be learnt. They tibink of aU empirical 
knowledge as consisting of inductions from a number of more 
or less similar experiences, For my part, I think that such a view 
makes history impossible and memory unintelligible. I hold that, 
from any occurrence that a man notices, he can obtain know- 
ledge, which, if his linguistic habits are adequate, he can express 
in sentences. His linguistic habits, of course, have been generated 
by past experiences, but these only determine the words he uses. 
The truth of what he says, given the meanings of his words, 
can, given adequate care, be wholly dependent upon the character 




of one occurrence that he is noticing. When this is the case 
what he is asserting is what I call a "basic proposition". 

The discussion of basic propositions has two parts. First it 
is necessary to argue, as against opposing opinions, that there 
are basic propositions. Secondly, it is necessary to determine just 
what sort of thing they can affirm, and to show that this is 
usually much less than common sense asserts on the occasions 
on which the basic propositions in question are epistemologically 

A basic proposition is intended to have several characteristics. 

must be known independently of inference from other pro- 
positions, but not independently of evidence, since there must 
be a perceptive occurrence which gives the cause and is con- 
sidered to give the reason for believing the basic proposition. 
Then again, from a logical point 

so to analyse our empirical knowledge that its primitive pro 
positions (apart from logic and generalities) should all have been, 
at the moment when they were first believed, basic propositions. 
This requires that basic propositions should not contradict each 
other, and makes it desirable, if possible, to give them a logical 
form which makes mutual contradiction impossible. These con- 
ditions demand, therefore, that a basic proposition should have 
two properties : 

of view, it should be possible 

(i) It must be caused by some sensible occurrence; 
(2) It must be of such a form that no other basic proposition 

can contradict it. 

As to (i): I do not wish to insist upon the word "caused", 
but the belief must arise on the occasion of some sensible occur- 
rence, and must be such that, if questioned, it will be defended 

by the argument 




belief refers to a certain time, and the 

see it" or something similar 


reasons for believing it 
did not exist before that time. If the event in question had been 
previously inferred or expected, the evidence beforehand was 
different from that afforded by perception, and would generally 
be considered less decisive. Perception affords for the belief 




^ I 


evidence which is considered the strongest possible, but which 
is not verbal. 

As to (2): the judgments that common sense bases upon 





there is a dog", usually go beyond the 

present datum, and may therefore be refuted by subsequent 
evidence. We cannot know, from perception alone, anything 










or about bodies understood in an impersonal sense. That 




in the search for data, we are driven to analy 

we are seeking a core which is logically independent of other 
occurrences. When you think you see a dog, what is really given 
in perception may be expressed in the words "there is a canoid 
patch of colour". No previous or subsequent occurrence, and 
no experience of others, can prove the falsehood of this pro- 


position. It is true that, in the sense in which we infer ec 
there can be evidence against a present judgment of perception 
but this evidence is inductive and merely probable, and cannot 


stand against 


the evidence of the senses 



n we 


analysed a judgment of perception in this way, we are left with 
something which cannot be proved to be false. 

We may then define a "basic proposition" as follows: it is a 
proposition which arises on occasion of a perception, which is 
the evidence for its truth, and it has a form such that no two 
propositions having this form can be mutually inconsistent 
derived from different percepts. 

Examples would be: "I am hot", "that is red", "what a foul 
smell". All basic propositions in the above sense are personal, 
since no one else can share my percepts, and transitory, for after 
a moment they are replaced by memories. 

In place of the above definition, we can adopt a logical defi- 
nition. We can consider the whole body of empirical knowledge, 
and define "basic propositions" as those of its logically indemon- 
strable propositions which are themselves empirical 
some temporal occurrence, 
sionally equivalent to the above epistemological definition. 

Some among logical positivists, notably Neurath and Hempel 



This definition, I think, is exten 






deny that any set of propositions can be singled out as "basic", 
or as in any important epistemological sense premisses for the 
remainder. Their view is that "truth" is a syntactical^ not a 
semantic concept: a proposition is "true'* within a given system 
if it is consistent with die rest of the system, but there may be 
other systems, inconsistent with the first, in which the proposition 
in question will be "false". There is no such process, according 
to diem, as deriving the truth of a proposition from some non- 
verbal occurrence : the world of words is a closed self-contained 
world, and the philosopher need not concern himself with any- 
thing outside it. 

In logic and mathematics, the view that "truth" is a syntactical 
concept is correct, since it is syntax that guarantees the truth 
of tautologies. Truth, in this sphere, is discoverable by studying 
the form of the proposition concerned ; there is no need to go 
outside to something that the proposition "means" or "asserts". 
The authors in question assimilate empirical to logical truth, thus 
reverting unconsciously to the tradition of Spinoza, Leibniz and 
Hegel. In rejecting their view, as I shall contend that we must, 
we are committing ourselves to the opinion that "truth" in 
empirical material has a meaning diflFerent from that which it 
bears in logic and mathematics. 

The coherence theory of truth, as I have just said, is that of 

Hegel. It is worked out, from a Hegelian point of view, in 

Joachim's .book The Nature of Truthy which I criticized, from 

the standpoinl>o£^the correspondence theory, in Philosophical 
Essays (1910). Thellegelian theory, however, differs from that 
of Neurath, since it holds that only one body of mutually coherent 
propositions is possible, so that every proposition remains defi- 
nitely true or false. Neurath, on the contrary, takes the view of 
Pirandello: "so it is, if you think so". 

The theory of Neurath and Hempel is set forth in articles in 
Erkemtnis and Analysis. The following are quotations or para- 
phrases of their words. 

An assertion is called right when we can fit it in 

(einglkderri) ^ 




Assertions are compared with assertions, not with "expe- 
riences'* (Erlebnissen). 

There are no primary Protokollsdtsre or propositions needing 
no confirmation. 

All Protokollsdtie should be put into the following form: 
"Otto's protocol at 3:17: {Otto's word-thought at 3:16 (In 
the room at 3:15 was a table perceived by Otto)}." 

Here the repeated use of the word "Otto" instead of "I" is 

Although, according to the above, it would seem as if we 
were debarred from knowing anything about the physical world 
except that physicists make certain assertions about it, Neurath 
nevertheless commits himself to the statement that sentences are 
mounds of ink or systems of air-waves (Erkermtnis IV, 209) . 
He does not tell us how he discovered this fact ; presumably he 
only means that physicists assert it. 

Neurath in "Radikaler Physikalismus und Wirkliche Welt" 
{Erkennmis IV, 5, 1934), maintains the following theses: 

I • All ReaUatie of science including ProtokollsatiCy are chosen 
as the result of Entschlusse (decisions), and can be altered. 
2. We call a Realsdti false when it cannot fit into the edifice 

of science. 

The control of certain Recdsdtie is compatibility with 

certain Protokollsdtie: instead of die Wirklichkeit we have a 
number of mutually incompatible but internally coherent 
bodies of propositions, choice between which is ^'nkht logisch 

The practice of life, Neurath says, quickly reduces ambiguity; 
moreover the opinions of neighbours influence us. 

Carl G. Hempel "On the logical positivist's theory of truth" 

{Analysis II, 4, Jan. 1935) sets forth the history of the views 

of logical positivists as to Protokollsdtie. He says the theory 
developed step by step from a correspondence theory into a 
restrained coherence theory. He says that Neurath denies that 
we can ever compare reality with propositions, and that Carnap 



We Started, he says, from Wittgenstein's atomic propositions • 
these were replaced by Protokollsdtie^ at first thought to express 
the results of observation. But then Protokollsdtie were no longer 
the result of observation, and then no class of statements was 
admitted as basic. 

Carnap (Hempel continues) says there are no absolutely first 
statements for science; even for Protokolhdtie further justifica- 
tion may be demanded. Nevertheless : 

"Carnap and Neurath do by no means intend to say: *There 
are no facts, there are only propositions*; on the contrary, the 
occurrence of certain statements in the protocol of an observer 
or in a scientific book is regarded as an empirical fact, and the 
propositions occurring as empirical objects. What the authors 
do intend to say, may be expressed more precisely thanks to 
Carnap's distinction between the material and the formal mode 
of speech. . . . 

"The concept of truth may be characterized in this formal 
mode of speech, namely, in a crude formulation, as a suflScient 
agreement between the system of acknowledged Protokolhdtie 
and the logical consequences which may be deduced from the 
statement and other statements which are already adopted 

# • 

Saying that empirical statements 'express facts* and conse- 
quently that truth consists in a certain correspondence between 
statements and the 'facts' expressed by them, is a typical form 
of the material mode of speech." (p. 54) [i.e., "truth'' is syntactic, 
not semantic] 

"In order to have a relatively high degree of certainty, one 
will go back to the Protokollsdtie of reliable observers." [Two 
questions arise : A. How do we know who are reliable > B. How 
do we know what they say ?\ 

"The system of Protokollsdtie we call true . . . may only be 
characterized by the historical fact, that it is the system which 
is actually adopted by mankind, and especially by the scientists 
of our culture circle. 

Protokollsati, like every other statement, is at the end 
adopted or rejected by a decision 




ProtokoUsdtie are now superfluous. It is implied that there 
is no definite world with definite properties* 

think Neurath and Hempel may be more or less right as 
regards their problem, which is the construction of an encyclo- 
paedia. They want public impersonal propositions, incorporated 
in public science. But public knowledge is a construction, con- 
taining less than the sum oi private knowledges. 

The man who is constructing an encyclopaedia is not expected 
himself to conduct experiments; he is expected to compare the 
opinions of the best authorities, and arrive, so far as he can, at 
the standard scientific opinion of his time. Thus in dealing with 
a scientific question his data are opinions, not direct observations 
of the subject-matter. The individual men of science, however, 
whose opinions are the encyclopaedist's premisses, have not 



themselves merely compared other investigators' opinions; they 
have made observations and conducted experiments, on the basis 
of which they have been prepared, if necessary, to reject pre- 
viously unanimous opinions. The purpose of an observation or 
experiment is to give rise to a perceptive experience, as a result 
of which the percipient has new knowledge, at first purely per- 
sonal and private. Others may repeat the experiment, and in 
the end the result becomes part of public knowledge ; but this 
public knowledge is merely an abstract or epitome of private 

All theory of knowledge must start from "what do / know ?'* 
not from "what does mankind know?" For how can I tell what 
mankind knows ? Only by (a) personal observation of what it 
says in the books it has written, and {b) weighing the evidence 

in favour of the view that what is said in the books is true. 

; if I am a 

student of cuneiform, I may decide that Darius did not say what 
he is supposed to have said about his campaigns. 

There is a tendency — not confined to Neurath and Hempel, 
but prevalent in much modern philosophy — to forget the argu- 
ments of Descartes and Berkeley. It may be that these arguments 
can be refuted, though, as regards our present question, 


am Copernicus, I shall decide against the books 





not believe that they can be. But in any case they are too weighty 
to be merely ignored. In the present connection, the point is that 
my knowledge as to matters of fact must be based upon my 
perceptive experiences, through which alone I can ascertain what 
IS received as public knowledge. 

This applies, in particular, to what is to be found in books. 
That Carnap's books say whatever they do say is the sort of 
thing that would be generally accepted as public knowledge. 

But what do I know? 

(i) What I see when I look at them 

(2) What I hear when others read them aloud 

(3) What I see when others quote them in print 


(4) What I see when I compare two copies of the same 

Hence, I pass, by elaborate and doubtful inferences, to public 


On Neurath's view, language has no relation to non-linguistic 
occurrences, but this makes many every-day experiences inex 

pKcable. For instance: I arrived in Messina from a sea voyage 

m 1901 and found flags at half-mast; on inquiry I learnt that 
McKinley had been murdered. If language has no relation to the 
non-linguistic, this whole procedure was frivolous. 

As we saw, Neurath says the proper form of a protocol sen- 
tence is: "Otto's protocol at 3:17: {Otto's word-thought at 

t6 was: (In the room at 3:15 there was a table perceived by 

It seems to me that, in giving this form to protocol sentences, 

Neurath shows himself far more credulous than the man who 
says "there's a dog". In the inside bracket he perceived a table, 
which is Just as bad as perceiving a dog. In the outside bracket 
he finds w^ords for what he has perceived, viz.: "in the room 
at 3 : 15 there was a table perceived by Otto". And a minute later 
he writes down die words at which he has arrived. This last 
stage involves memory and the continuity of the ego. The second 
stage , involves memory also, and in addition involves intro- 





Let us take the matter in detail. 

To begin with the inner bracket: "in the room at 3:15 there 
was a table perceived by Otto". We may take the words "in 


the room" as merely meaning that the table had a perceptual 
background, and in that sense they may be allowed to pass. The 
words "at 3:15" imply that Otto was looking at his watch as 
well as at the table, and that his watch was right. These are grave 
matters, if taken seriously. Let us suppose that, instead of "at 
3:15" we say "once upon a time", and instead of "3:16" we 
say "a little later", and instead of "3 riy" we say "a little later 
still". This eliminates the difficulties of time-measurement, which 
surely Neurath cannot have intended to introduce. We come now 
to the words "there was a table". These are objectionable on the 
same grounds as "there's a dog". It may not have been a table, 
but a reflection in a mirror. Or perhaps it was like Macbeth*s 
dagger, a phantasm called up by the intention of committing 
a murder on a table. Or perhaps a very unusual collocation of 
quantum phenomena caused a momentary appearance of a table, 
which was going to disappear in another moment. It may be 
conceded that this last hypothesis is improbable, that Dr. Neurath 
is not the sort of person who would think of murdering anybody, 
and that his room probably contains no mirror large enough for 
the reflection of a table that is elsewhere. But such considerations 
ought not to be necessary where protocol-sentences are con- 

I come now to a still more serious matter. We are told, not 
only that there was a table, but that there was a table "perceived 
by Otto". This last is a social statement, derived from experience 
of social life, and by no means primitive ; in so far as there is 
reason to believe it, it is based upon argument. Otto perceives 
the table, or rather a tabular appearance — ^well and good — ^but 
he does not perceive that Otto perceives it. What is "Otto".^ 
So far as he can be known, either to himself or others, he is 
a series of occurrences. One of them is the visual appearance 
which he rashly calls a table. By the help of conversation, he is 
led to the conclusion that the occurrences peop le mention form 




bundles, each of which is one person, and that the appearance 
of the table belongs to the same bundle as the subsequent word* 
thought and the still more subsequent act of writing. But all this 
elaboration is no part of the visual datum. If he always lived 
alone, he would never be led to distinguish between "there's 

a table" and "I see a table**; in fact, he would always use the 
former phrase, if one could suppose him using phrases at all 
The word "P* is a word of limitation, meaning **I, not you"; 
it is by no means part of any primitive datum. And this is 
still more evident when, instead of "F*, Neurath says 

So far we have only heen concerned with what happened 

at 3:15. It is now time to consider what happened at 

At 3:16, Otto put into words what had happened at 3:15 

Now I am willing to admit that the words he used are such as 
well might be employed by a man who was not on the lookout 
for pitfalls. There is, therefore, less to criticize at this stage. What 
he diought may well not have been true, but I am quite willing 
to concede that he thought it, if he says so. 

At 3:17, Otto carried out an act of introspection, and decided 
that, a minute ago, a certain phrase had been in his thoughts, 
not just as a phrase, but as an assertion concerning an earlier 
perception which, at 3:1 6, he still remembered. It is only what 
happens at 3:17 that is actually asserted. Thus according to 

Neurath the data of empirical science are all of the following 

certain person (who happens to be myself, but this, we 
are told, is irrelevant) is aware at a certain time that a little while 
ago he believed a phrase which asserted that a litde while before 
that he had seen a table." 

That is to say, all empirical knowledge is based upon recol- 
lections of words used on former occasions. Why recollections 
should be preferred to perceptions, and why no recollections 
should be admitted except of thought-words, is not explained. 
Neurath is making an attempt to secure publicity in data, but 




by mistake has arrived at one of the most subjective forms of 
knowledge, namely recollection of past thoughts. This result 
is not encouraging to those who believe that data can be 

The particular form given to protocol-sentences by Neurath 
is, perhaps, not an essential part of his doctrine. Let us therefore 
examine it more generally. 

Let us repeat some quotations 



ments are compared 

with statements, not with experiences" (N). "A protocol-state 
ment, like every other statement, is at the end adopted or rejected 

by a decision 


The system of ProtokollsatTc we call true 

may only be characterized by the historical fact, that it is 
the system which is actually adopted by mankind, and especially 

by the scientists of our culture circle 



Instead of reality 

we have a number of mutually incompatible but internally 
coherent bodies of propositions, choice between which is not 
logically determined {logisch ausgeiekhnety (N). 

This attempt to make the linguistic world self-sufficient is 
open to many objections. Take first the necessity of empirical 

statements* about words 




Neurath says so-and-so 


do I know this ? By seeing certain black marks on a white ground. 
But this experience must not, according to Neurath and Hempel, 
be made a ground for my assertion that Neurath says so-and-so. 
Before I can assert this, I must ascertain the opinion of mankind, 
and especially of my culture circle, as to what Neurath says. But 
how am I to ascertain it } I go round to all the scientists of my 

reply I hear certain sounds, but this is an experience, and there- 
fore does not give any ground for an opinion as tojvhat they 

^ and the 

culture circle, and say: "what does Neurath say on p. 364 

said. When A answers, I must go round to 

rest of my culture circle, to ascertain what they think A said 

And so on throughout an endless 

If eyes and ears do 


not enable me to know what Neurath said, no assemblage of 

scientists, however distinguished 

can enable me to know 


Neurath is right, his opinions are not known to me throx^h his 

In what follows, "N" stands for "Neurath" and "H" for "Hempel". 



writings, but through my decisions and those of my culture circle. 
If we choose to attribute to him opinions completely different 
from those which he in fact holds, it will be useless for him to 
contradict, or to point to pages in his writings; for by such 
behaviour he will only cause us to have experiences, which are 
never a ground for statements. 

Hempel, it is true, denies such consequences of his doctrine* 
He says: "Carnap and Neurath do by no means intend to say: 
'there are no facts, there are only propositions' ; on the contrary, 
the occurrence of certain statements in the protocol of an observer 
or in a scientific book is regarded as an empirical fact, and the 
propositions occurring as empirical objects," But this makes non- 
sense of the whole theory* For what is an "empirical fact"? To 
say: "A is an empirical fact" is, according to Neurath and Hempel, 
to say: "the proposition *A occurs' is consistent with a certain 

body of already accepted propositions". In a different culture 
circle another body of propositions may be accepted ; owing to 
this fact, Neurath is an exile* He remarks himself that practical life 
soon reduces the ambiguity, and that we are inifiuenced by the 
opinions of ndghboui In ote words, empirical .rud, can be 

determined by the police* This doctrine, it is evident, is a com- 
plete abandonment of empiricism, of which the very essence is 

that only experiences can determine the truth or falsehood of 
non-tautologous propositions. 

Neurath's doctrine, if taken seriously, deprives empirical pro- 
positions of all meaning. When I say "the sun is shining", I 
do not mean that this is one of a number of sentences between 
which there is no contradiction; I mean something which is not 
verbal, and for the sake of which such words as "sun" and 

"shining" were invented. The purpose of words, though philo- 
sophers seem to forget this simple fact, is to deal with matters 
other than words. If I go into a restaurant and order my dinner, 
I do not want my words to fit into a system with other words 

but to bring about the presence of food. I could have managed 
without words, by taking what I want, but this would have been 
less convenient The verbalist theories of some modem philo- 



sophers forget the homely practical purposes of every-day words 
and lose themselves in a neo-neo-Platonic mysticism. I seem to 

hear them saying "in the beginning was the Word", not "in the 
beginning was what the word means". It is remarkable that this 
reversion to ancient metaphysics should have occurred in the 
attempt to be ultra-empiricaL 





Chapter XI 


Assuming, as I shall do henceforth, that there are basic pro- 
positions, it seems to me that, for theory of knowledge, "basic 
propositions" may be alternatively defined as "those propositions 
about particular occurrences which, after a critical scrutiny, we 
still believe independently of any extraneous evidence in their 

Let us consider the clauses of this definition, and let us begin 
at the end. There may be evidence in favour of a basic proposition, 
but it is not this evidence alone that causes our belief. You may 
wake up in the morning and see that it is daylight, and you may 
see from your watch that it must be daylight. But even if your 
watch pointed to midnight, you would not doubt that it is day- 
light. In any scientific system, a number of propositions based on 
observations support each other, but each is capable of com- 
manding belief on its own account. Moreover mutual support 

among basic -propositions is only possible on the basis of some 

There are cases, however — chiefly where memory is concerned 
in which our belief, though not inferential, is more or less un- 
certain. In such cases, a system composed of such beliefs wins 

more acceptance than any one of them singly. I think Mr. Z. 
invited me to dinner on Thursday; I look in my diary, and find 
an entry to that effect. Both my memory and my diary are fallible, 
but when they agree I think it unlikely that they are both wrong. 
I will return to this kind of case later; for the present, I wish to 
exclude it. It is to be observed, meantime, that a non-inferential 

, ...^^.^wx^^v,, 

belief need not be either certain or indubitable. 

Now comes the question of critical scrutiny, and a very 


awkward question it is. You say "there^s a dog", and feel quite 
satisfied of the truth of your statement. I shall not suppose your 
faith attacked by Bishop Berkeley, but by one of his allies in 

modern business. The producer comes to you and says: "ah, 
hoped you would think it was a dog, but in fact it was recorded 
by the new system of technicolour, which is revolutionizing the 
cinema". Perhaps the physiologist in future will be able to stimu- 
late the optic nerve in the way necessary for seeing a dog; 
have gathered from the works of Bulldog Drummond that con- 
tact of a fist with the eye enables people to see the starry heavens 
as well as the moral law. And we all know what hypnotists can 
do; we know also how emotional excitement can produce pheno- 
mena like Macbeth's dagger. On these grounds, which are all 
derived from common sense, not from philosophy, a man pos- 
sessed of intellectual prudence will avoid such rash credulity as 
is involved in saying "there's a dog". 

But what, then, will such a man say on such an occasion? 
Having been badly brought up, he will have an impulse to say 
"dog'\ which he will have to restrain. He will say: "there is a 
canoid patch of colour". Suppose, now, having been impressed 
by the method of Cartesian doubt, he tries to make himself 
disbelieve even this. What reason can he find for disbelieving it? 
It cannot be disproved by anything else that he may see or hear; 
and he can have no better reason for believing in other sights or 
sounds than in this one ; if he carries doubt to this length, he 
cannot even know that he said "dog'*, if he did say so. 

We should note that basic propositions must be just as true 
when applied to dreams as when applied to waking life; for, 
after all, dreams do really occur. This is a criterion for dis- 
criminating between what is basic and what is interpretative. 

We thus arrive at the momentary object of perception as the 
least questionable thing in our experience, and as therefore the 
criterion and touchstone of all other certainties and pseudo- 

But for theory of knowledge it is not sufficient that we should 
perceive something; it is necessary that we should express what 





) i 



we perceive in words. Now most object-words are condensed 
inductions; this is true of the word "dog", as we have already 
had occasion to notice. We must avoid such words, if we wish 
to be merely recording what we perceive. To do this is very 
difficult, and requires a special vocabulary. We have seen that 
this vocabulary includes predicate-words such as "red", and 
relation-words such as "precedes", but not names of persons or 
physical objects or classes of such terms. 

We have considered the subject of "basic propositions" or 
Protokollsdtie^ and tried to show that empirical knowledge is 
impossible without them. It will be remembered that we defined 
a "basic proposition" by t\^^o characteristics: 

(i) It arises on occasion of a perception, which is the evidence 

for its truth; 

(2) It has a form such that no two propositions having this 

form can be mutually inconsistent if derived from different 


proposition having these two characteristics cannot be 

disproved, but it would be rash to say that it must he true. 

Perhaps no actual proposition quite rigidly fulfils the definition. 
But pure perceptive propositions remain a limit to which we can 
approach asymptotically, and the nearer we approach the smaller 

is the risk of error. 

Empirical knowledge requires, however, other premisses 
asserting matters of fact, in addition to pure perceptive proposi- 
tions. I shall give the name "factual premiss" to any uninferred 
proposition which asserts something having a date, and which I 

believe after a critical scrutiny. I do not mean that the date is 
part of the assertion, but merely that some kind of temporal 
occurrence is what is involved in the truth of the assertion. 

Factual premisses are not alone sufficient for empirical know- 
ledge, since most of it is inferred. We require, in addition, the 
premisses necessary for deduction, and those other premisses, 
whatever they may be, that are necessary for the non-demon 
strative inferences upon which science depends. Perhaps there 
are also some general propositions such as "if A precedes 


nd B precedes C, then A precedes C" and "yellow is more like 

5*reen than like blue". Such propositions, however. 



nentioned, call for a lengthy discussion. For the 




Dnly concerned with those premisses of our empirical knowledge 
:vhich have to do with particular occurrences, i.e., with* those that 
am. calling "factual premisess". These, it seems to me, are of 
"our kinds: 

. Perceptual propositions. 
11. Memory propositions. 

III. Negative basic propositions. 

IV. Basic propositions concerning present propositional 
attitudes, i.e. concerning what I am believing, doubting, desiring, 


. Perceptual Propositions. Suppose, as in an earlier chapter, 

that we see a red square inscribed in a blue circle. "We may say 
"there is a square in a circle", "there is a red figure in a blue one", 

> Ba&i-i 

"there is a red square in a blue circle". All these are judgments of 
perception. The perceptual datum always allows many proposi- 
tions, all expressing some aspect of it. The propositions are more 
abstract than the datum, of necessity, since words classify. But 
there is no theoretical limit to the accuracy of specification that 
is possible, and there is nothing in the perceptual datum that is 
essentially incapable of being expressed in words. 

The correspondence theory of truth, as applied to judgments 
of perception, may be interpreted in a way which would be false. 
It would be a mistake to think that, corresponding to every true 
judgment of perception, there is a separate fact. Thus in the above 
case of the circle and the square, there is a circle of a certain colour 
and of certain angular dimensions, and inside it there is a square 
of a certain other colour and of certain other angular dimensions* 
All this is only one datum, from which a variety of judgments of 
perception can be derived. There is not, outside language, a fact 
"that there is a square in a circle'', and another fact "that there is 
a red figure in a blue figure". There are no facts "that so-and-so", 



There are percepts, from which, by analysis, we derive proposi- 
tions "that so-and-so". But so long as this is realized, it will do 
no harm if percepts are called "facts". 

11. Memory Propositions. There are considerable difficulties 
about basic propositions of this class. For, first, memory is fallible, 
so that in any given case it is difficult to feel the same degree of 
certainty as in a judgment of perception; secondly, no memory 
proposition is, strictly speaking, verifiable, since. nothing in the 
present or the future makes any proposition about the past 
necessary; but thirdly, it is impossible to doubt that there have 
been events in the past, or to believe that the world has only just 
begun. This third consideration shows that there must be factual 
premisses about the past, while the first and second make it 
difficult to say what they are. 

I think, to begin with, that we must exclude from the category 
of memories what we know about the immediate past. For instance, 
when we see a quick movement, we know that the object con- 
cerned was in one place and is in another; but this is all to be 
included in perception, and cannot be counted as a case of memory. 
This is shown by the fact that seeing a movement is different 
from seeing a thing first in one place and then in another.* 

is by no means easy to distinguish between memory and 


habit; in ordinary speech, the distinction is ignored where 
verbal habits are concerned. A child is said to "remember" the 
multiplication table if he has the correct verbal habits, although 
the multiplication table never happened and he may not remember 
any of the occasions on which he learnt it. Our memory of past 
events is sometimes of the same sort : we have a verbal habit of 
narrative, but nothing more. This happens especially with inci- 
dents that one relates frequently. But how about past incidents 
that one has never recalled till now, or at any rate not for a long 
time? Even then, the memory may be recalled by association, 


Ah, yet doth beauty, like a dial-hand, 
Steal from his figure, and no pace perceived. 

[Shakespeare, Sonnet CIV.] 






which is a form of habit. Turgenev's Smoke opens with the smell 
of heliotrope recalling a long-past love affair. Here the memory is 
involuntary; there is, however, also deliberate recollection, for 
example in writing an autobiography. I think that association is 
still the main agent here. We start from some prominent incident 
that we remember easily, and gradually associations lead us on 
to things that we had not thought of for a long time. The pro 
minent incident itself has remained prominent, usually, because 
it has many associative links with the present. It is obvious that 
we are not always remembering everything that we can remember 
and that what causes us to remember a given occurrence at a 
given moment is some association with something in the present. 
Thus association is certainly a vital factor in the occurrence of a 
recollection. But this leaves us still in doubt as to the epistemo- 

logical status of memory. 

Take, first, the fact that we know what is meant by the past. 
Would this be possible without memory.'* It may be said that 
we know what is meant by the future, although we have no 
memory of it. But I think the future is defined by relation to the 
past: it is "a time when what is now the present is past". Lapse 

be understood from the specious 

"dinner is 

sentence, say 

of time, up to a point, can 
present: when a person utters a short 
served'', we know there is a lapse of time between the first word 
and the last, though the whole sentence comes within the specious 
present. But in true memory there is a pastness of an altogether 
different kind, and this is something with which association has 
nothing to do. Say you meet a man whom you have not seen for 
twenty years : association will account for any words or images 
connected with the previous meeting that may come into your 
mind, but will not account for the reference of these words or 
images to the past. You may find it impossible to refer them to 
the present, but why not treat them as mere imaginative fantasies ? 
You do not do this, but treat them as referring to something that 

would seem, therefore, that the mere fact 

really happened. 

that we can understand the word "past" implies knowledge that 

something happened in the past. Since it is hardly possible that 




our most primitive knowledge of the past should refer to a vague 
"something", there must be more definite memories which are 
to be accepted as basic propositions. 

Let us take some recollection that it is very difficult to doubt. 
Suppose you receive a telegram to say that your uncle in Aus- 
tralia has left you a million pounds, and you go upstairs to tell 
your wife. By the time you reach her, your first reading of the 
telegram has become a memory, but you can hardly doubt that 
it occurred. Or take more ordinary events : at the end of the day, 
you can recall many things that you have done since you got up, 
and concerning some, at least, you feel a high degree of certainty. 
Suppose you set to work to remember as many as you can. 
There are things that you know because they aways happen: 
that you dressed, breakfasted, and so on. But in regard even to 
them, there is a very clear difference between knowing that they 
must have occurred and remembering them. It seems to me that, 
in true memory, we have images to which we say "y^^" ^^ "no". 
In some cases, we say "yes" emphatically and without hesitation; 
in others, we depend partly upon context. For our purpose, the 
emphatic cases are the important ones. Images come, it seems to 
me, in three ways : as merely imaginary, or with a yes-feeling, or 
with a no-feeling. When they come with a yes-feeUng, but do not 
fit into the present, they are referred to the past. (I do not mean 
that this is a complete account of what happens in memory.) 
Thus all memory involves propositional attitudes, meaning, and 
external reference; in this it differs from judgments of perception. 

No memory is indubitable. I have had memories in dreams, 
just as definite as the best memories of waking life, but wholly 

untrue. I once, in a dream, remembered that Whitehead and I 

, *** « ^S.^^M.^y 

had murdered Lloyd George a month ago. Judgments of per- 
ception are just as true when applied to dreams as when applied 

to waking life; this, indeed, is a criterion for the correct inter- 
pretation of judgments of perception. But memory judgments in 
dreams, except when they consist in remembering an earlier part 
of the dream or a real event of waking life, are erroneous. 

Since memories are not indubitable, we seek various ways of 



reinforcing them. "We make contemporary records, or we seek 
confirmation from other witnesses, or we look for reasons 
tending to show that what we recollect was what was to be 
expected. In such ways we can increase the likelihood of any 
given recollection being correct, but we cannot free ourselves 
from dependence on memory in general This is obvious as 
regards the testimony of other witnesses. As regards contem- 
porary records, they are seldom strictly contemporary, and 
they are, it cannot be subsequently known except through the 
memory of the person making the record. Suppose you remember 
on November 8th that last night you saw a very bright meteor, 
and you find on your desk a note in your handwriting saying: 
"at 2oh. 32m. G.M.T. on November 7th, I saw a bright meteor 
in the constellation Hercules. Note made at 2oh. 33m. G.M.T.*' 
You may remember making the note; if so, the memory of the 
meteor and the note confirm each other. But if you are discarding 
memory as a source of knowledge, you will not know how the 
note got there. It may have been made by a forger, or by your- 
self as a practical j oke. As a matter of logic, it is quite clear that 
there can be no demonstrative inference from a set of shapes now 
seen on paper to a bright light seen in the sky last night. It would 
seem, therefore, that, where the past is concerned, we rely 
partly on coherence, and partly on the strength of our conviction 
as regards the particular memory which is in question ; but that 
our confidence as regards memory in general is such that we cannot 
entertain the hypothesis of the past being wholly an illusion. 

It will be remembered that, in an earlier chapter, we decided 
diat memory propositions often require the word "some". We 
say "I know I saw that book somewhere'*, or "I know he said 
something very witty'*. Perhaps we can remember even more 

vaguely, for instance "I know something happened yesterday 
We might even remember "there have been past events'*, which 
we rejected as a factual premiss a little while ago. I think that to 
accept this as a factual premiss would be going too far, but 
there certainly are uninferred memory propositions (at any given 
moment) which involve "some**. These are logically deducible 



from propositions not involving "some" which were, at some 
previous time, expressions of present perception. You say to 
yourself one day "oh there is that letter I had lost", and next 
day "I know I saw that letter somewhere yesterday". This is an 
important logical difference between memory and perception, 
for perception is never general or vague. When we say it is vague, 
that only means that it does not allow so many inferences as 
some other perception would allow. But images, in their repre- 
sentative capacity, may be vague, and the knowledge based upon 

them may involve the word "some". It is worthy of note that 
this word may occur in a factual premiss. 

In admitting memory propositions among factual premisses, 
we are conceding that our premisses may be doubtful and some- 
times false. We are all willing, on occasion, to admit evidence 
against what we think we remember. Memories come to us with 
different grades of subjective certainty; in some, there is hardly 
more doubt than as regards a present percept, whereas in others 
the hesitation may be very great. Memories, in practice, are 
reinforced by inferences as casual as is possible, but such inferences 
are never demonstrative- It would be a great simplification if we 

could dispense with memory premisses, or if, failing that, we 
could distinguish two kinds of memory, of which one is in- 
fallible. Let us examine these possibilities. 

In an attempt to dispense with memory, we shall still allow 
knowledge of whatever falls within the specious present; thus 
we shall be still aware of temporal sequence. We shall know 
what is meant by "A is earlier than B". We can therefore define 
"the past" as "what is earlier than the specious present". We 
shall construct our knowledge of the past by means of causal 
laws, as we do in geology, where memory does not come in. 
We shall observe that we have a habit of making a record of an 
event that for any reason is important to us, either in writing or 

creating in ourselves a verbal habit. We do the latter, for 

example, if, when we are introduced to a man, we repeat his 
name over and over to ourselves. We may do this so often that, 
when we next see him, we think of his name at once. We are then 



: ri^^"^' 




in popular language, to ** remember" his name, but we do 
)t necessarily recall any past event. Is it possible to build up 
ir knowledge of the past in this way, by means of records and 
?rbal habits alone ? In this view, if I see a man and know that 
s name is Jones, I shall infer that I must have met him on some 
rmer occasion, just as I do if his face is vaguely familiar. When 
see a record, I can know that it is in my handwriting without 


,^■1 ■■I'.i' -^' ; 


■r i.. ' 
-•'.' I. 





ilBBt I 


aving to invoke recollection, because I can copy the record 
ow and make comparisons; I can then go on to infer that the 
cord tells' of something that once happened to me. In theory, 
le small but finite stretch of time comprised within the specious 
resent should suffice for the discovery of causal laws, by means 
f which we could infer the past without having to appeal to 

I am not prepared to maintain that the above theory is logically 
mtenable. There is no doubt that we could, without the help 
Df memory, know something of the past. But I think it is clear 
:hat, in fact, we know more of the past than can be accounted 
ibr in this way. And while we must admit that we are sometimes 
nistaken as to what we think we remember, some recollections 
are so nearly indubitable that they would still command credence, 

ri SKf' 


",-, .. . 




ri.' .1 


aven if much contrary evidence were produced. I do not see, 
therefore, on what ground we could reject memory as one 

of the sources of our knowledge concerning the course of 

It remains to inquire whether there are two kinds of memory, 
one fallible and one infallible. We might maintain this without 
maintaining that we could know infallibly to which kind a given 
recollection belonged ; we should then still have reason for some 
degree of uncertainty in every particular case. But we should at 
least have reason to think that some memories are correct. The 
theory, therefore, is worth examining. 

I should not have considered seriously the possibility of there 
being two kinds of memory of which one is infallible, but for the 
fact that I Beard this theory advocated in discussion by G. E. 
Moore. He did not then elaborate it, and I do not know how 

\' -f 

■^ -. 





tenaciously he held it, I shall, tlierefore,, independently attempt to 

ive it as much plausibility as I can. 
It must be held, on logical grounds^ that no occurrence gives 

demonstrative grounds in favour of belief in any other occurrence. 
But the grounds are often sucli at> we cannot fail to accept as 
giving practical certainty- We saw that there cm. be no reason 
r disbelieving the proposition **ihat is red*' when made in 

tile presence of a red percept ; it must, liowever^ be admitted that 
belief in this proposition is logicaliy possible in the absence of 

a red percept, Sucli grounds as t%x%x for supposing that this docs 

not occur are derived from causal lawn as to the occurrence of 
language. We can^ however, in theory, distinguisli two cases in 
relation to a judgment such as **that is red'': one, wlaen it is 
caused by what it asserts^ and the other wlien wH>rds or images 
enter into its causation. In the former case it mu^;t be true^ in the 

latter not- 
This, however, is a statement whicli needs elaborating, Wliat 

can be meant when we say that a percept **causcH*' a word or a 
sentence? On the face of it, w^e have to suppose a considerable 

process in the brain, connecting visual centres with motor centres 
the causation^ therefore^ is by no means direct. Perhaps we may 
state the matter as follows: in the course of learning tn speak, 

certain causa! routes (language- hafaitn) are esiiabhshed in the 
brain^ which lead from percepts to utterances* These are the 

shortest possible routes from percepts to utterances; all others 
involve some further association or habit* Wlien an utterance is 
associated with a percept by a minimal caus^a! route-, tlie percept 
is said to be the **meaning** of the utterance^ mi the utterance is 
**true** because what it means occurs* Thus wlierever tliis state 

the truth of a judgmeni of perception h logically 

inquire whether anyiliing similar is possible in 

tlie case of memory* 

The stimulus to a judgment of recollection is obviously never 
the event 
The stimulus may be a percept, or may be a '^thought**. Let us 

since that is in the not immediate past 


ft • 


»-/ / 

. . J ., ■- 

<'''s^^ i 


ike the former case as the simpler. You jfind yourself, let us 

ippose, in some place where an interesting conversation occurred, 
id you remember the conversation. The cerebral mechanism 
volved is as yet hypothetical, but we may suppose it very 

imilar to that involved in the passage from a percept to a word 

occur together 

vhich **means*' it. When two percepts A and 
ne occurrence of a percept closely similar to A on a future occa- 
ion may cause an image closely similar to B, It may be argued 
hat a certain type of association between a percept like A and 
.n image like B can only occur if, on a previous occasion, A and 

3, as percepts, have occurred together, and that, therefore, the 


ecoUection resulting from the percept resembling A must be 

memories occur, it may 

be said, the 

orrect* Where fallacious 
associative causal chains involved must be longer than in the case 
of correct memories. Perhaps, in this way, the case of memory 
:an be assimilated to that of perception. 

The above type of argument, however, while it may be correct 
at its own level, can have no direct relevance to the question of 
factual premisses, since it presupposes elaborate knowledge con- 


the brain 




obviously, can only be built up 

means of factual premisses some of which are recollections. 

It must be admitted that a factual premiss need not be indubi 
tabkj even subjectively; it need only command a certain degree 
of credence. It can therefore always be reinforced if it is found to 
harmonize with other fa€iuil.,pxeinisses* What characterizes a 
factual premiss is not indubitability, but the fact that it com- 
mands a greater or less degree of belief on its own account, inde- 
pendently of its relations to other propositions- We are thus led 
to a combination of self-evidence with coherence : sometimes one 
factor is very much mote important than the other, but in theory 

always plays some part* The coherence required, 



however^ is not strict logical coherence 
can and should fc^ so stated as to be deductively independent of 
each other* The kind of coherence involved is a matter which I 
shall consider at a later stage* 






' W.l 



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>!■■ ^ ■) \- 

'-'■.' I. 












\* N 







J.. .1 




: f 



III. Negative Basic Propositions. We have already had occasion 

to consider negative empirical propositions, but I want now to 
consider afresh whether they are ever themselves factual pre- 
misses, or are always derived from incompatibility propositions. 
The question to be considered is: how do we know negative 
empirical propositions, such as *' there is no cheese in the larder'' 
or "there are no snakes in Ireland"? We entertained the hypo- 
thesis, when we considered this question in an earlier chapter 
that such propositions are inferred from premisses among which 
there are propositions such as "where there is red there is not 

yellow", or "what feels hard does not feel soft*'* I want now 
to examine afresh the whole question of negative empirical 

It is plain, to begin with, that sensible qualities fall into genera. 
There are colours, there are sounds, there are smells and tastes. 

there are various sorts of sensations of touch, there are sensations 
of temperature. As to these, certain things are to be noted. We 
can see two colours at once, but not in the same place. We can 
hear two sounds at once, and there need be no discoverable 
difference in their direction of origin. Smells have no location 
except in the nose, and two smells are not essentially incompatible, 
sensation of touch has qualities of which we may note two 

kinds : a local quality^ according to the part of the body touched 
and_a ^^Ikjr^' greater or less pressure j in each kind, different 
2iey des have the sort of incompatibility that colours have, i.e. 
on th|an be experienced simultaneously, but not in the same place 

It ie surface of the body. The same applies to temperature. 

diffe^thus appears that, as regards incompatibility, there are 

as r%ices between qualities belonging to different senses. But 

some Ms negative judgments there are no such differences 

ripe Goe brings you, in the dark, into the neighbourhood of a 

no. Wbgonzola, and says "can*t you smell roses .^" you will say 

lark, ^n you hear a foghorn, you know it is not the song of the 

awar(gid when you smell nothing or hear nothing, you can be 



ne5^ of the fact. It seems that we must conclude that pure 
'^ative propositions can be empirically known without being 


kh^ n - 

N*fi '^Iv'* p-^*^ 

- - I ^ V 




iferred. "Listen. Do you hear anything?*' 




othing recondite about this conversation. When you say '"no" 
1 such a case, are you giving the resuk of an inference, or are 
ou uttering a basic proposition? I do not think this kind of 
mowledge has received the attention that it deserves. If your 
no" gives utterance to a basic proposition (which must obviously 
DC empirical), such propositions may not only be negative, but 
pparently general, for your "no" may, if logic is to be believed 

■; % /'- 

36 expressed in the form: "all sounds are unheard by me now".* 
Thus the logical difficulties of general empirical knowledge will 



DC greatly lessened. If, on the other hand, your 
an inference, it must use some general premiss, for otherwise 
lo general conclusion could be inferred; and thus we shall still 
lave to admit that some basic propositions not belonging to 

logic are general. 


a person says 





and then you hear no sound 


you are in a condition to notice a noise if there were one. But this 
does not always apply, "Didn't you hear the dinner-bell ?" "No, 


was working." Here you have a negative memory judgment, 


and a cause (not a ground) assigned for its truth ; and 


case you are sure of the negative although you were not listening 
at the time. 

The conclusion seems irresistible that a percept or a memory 
may give rise to a negative factual premiss as well as to a positive 
one. There is an important difference: in the case of a positive 
basic proposition, the percept may cause the words, whereas in 
the case of a negation the words, or corresponding images, must 
exist independently of the percept. A negative basic propositio 
thus requires a propositional attitude, in which the propositi 
concerned is the one which, on the basis of perception, is deni 
We may therefore say that, while a positive basic proposition 
caused only by a percept (given our verbal habits), a negativ 
one is caused by the percept plus a previous propositional attitude. 
There is still an incompatibility, but it is between imagination and 



I shall argue later that theory of knowledge need not accept this logical 






lA'S. - 



perception. The simplest way of expressing this state of affairs 
is to say that, in consequence of perception, you know that a 
certain proposition is false. In a word : it is possible, in a certain 
sense, to notice what is not there as well as what is there. This 
conclusion, if true, is important. 

IV. Factual Premisses concerning present propositional attitudes. 

These propositions, just as much as "this is red", report a present 
occurrence, but they differ from basic propositions of Class I by 
their logical form, which involves mention of a proposition. 
They are propositions asserting that something is believed, 
doubted, desired, and so on, in so far as such propositions are 
known independently of inference. The something believed or 
doubted or desired can only be expressed by means of a sub- 
ordinate proposition. It is clear that we can be aware of believing 
or desiring something, in just as immediate a way as we can be 
aware of a red patch that we see. Some one says, let us suppose, 
"is to-day Wednesday.'^" and you reply "I think so'\ Your 
statement "I think so" expresses, in part at least, a factual premiss 
as to your opinion. The analysis of the proposition offers diffi- 
culties, but I do not see how to deny that it contains at least a 
kernel which expresses a datum. 

It will be observed that propositions of this class are usually, 
if not always, psychological. I am not sure that we could not use 

this fact to define "psychology". It might be said that dreams 
belong to psychology, and that basic propositions concerning 
percepts in dreams are exactly on a level with other basic pro- 
jiositipiis concerning percepts. But to this it may be replied that 
the-^cientific study of dreams is only possible when we are awake, 
and that, therefore, all the data for any possible science of dreams 
are memories. Similar answers could be made as regards the 
psychology of perception. 

However that may be, there is certainly an important depart- 
ment of. knowledge which is characterized by the fact that, 
among its basic propositions, some contain subordinate pro- 



The factual premisses considered in the above discussions all 
ave in common a certain characteristic, namely that they each 
afer to a short period of time, which is that at which they (or 
ther propositions from which they are deducible) first became 
remisses. In the case of recollections, if they are veridical, they 
re either identical with or logically inferrible from judgments 
f perception made at the times to which the recollections refer. 
3ur knowledge of the present and the past consists partly of 
>asic propositions, whereas our knowledge of the future consists 
/holly of inferences — ^apart, possibly, from certain immediate 

An "empirical datum" might be defined as a proposition 
referring to a particular time, and beginning to be known at the 
ime to which it refers; this definition, however, would be 

nadequate, since we may infer what is now happening before 
Tre perceive it. It is essential to the conception of an empirical 
latum that the knowledge should be (in some sense) caused by 

1^. .'■ '■' - ',•: 



are generally admitted, but it 

j^^hat is known. I do not wish, however, to introduce the con 

:eption of cause by a back door, and I shall therefore, at present 
'gnore this aspect of empirical knowledge. 

Among the premisses of our knowledge there must be pro- 
oositions not referring to particular events. Logical premisses 
ooth deductive and inductive 
seems possible that there are others. The impossibility of two 
different colours in the same part of the visual field is perhaps 
one. The question of propositions of this sort is difficult, and I 
will say nothing dogmatic about them. 

I will observe, however, that empiricism, as a theory of know- 
ledge, is self-refuting. For, however it may be formulated, it 
must involve some general proposition about the dependence of 
knowledge upon experience; and any such proposition, if true 
must have as a consequence that itself cannot be known. While. 

■ ' L ^ ■ ■ ■ ^ 

v-1 '1/ -.■".- 



therefore, empiricism may be true, it cannot, if true, be known 
to be so. This, however, is a large problem. 





^ I 

I J 
', ' 






' , J 

Chapter XII 




' I ' 


1 I 

' I 



The purpose of the present chapter is to state problems, not to 
solve them. Attempts at solution will be given in subsequent 

The first question is: does logic or theory of knowledge 
need "propositions" as well as "sentences" ? Here we may define 
a "proposition", heuristically, as "what a sentence signifies". 
Some sentences are significant, others are not; it is natural, 
though perhaps mistaken, to suppose that, when a sentence is 
significant, there is something that is its significance. If there is 
such a something, it is what I mean by the word "proposition". 

Since "having the same significance" is a relation which can 

certainly hold between two sentences — e.g. "Brutus killed 
Caesar" and "Caesar was killed by Brutus" — ^we can make sure 
of some meaning for the word "proposition" by saying that, 
we find no other meaning for it, it shall mean "the class of all 
sentences having the same significance as a given sentence". 

Whether or not there is a substantive "significance", there is 
certainly an adjective "significant". I apply this adjective to any 
sentence that is not nonsense. "Significant" and "significance" 
are words that I apply to sentences, whereas "meaning" is a 
word that I apply to single words. This distinction has no basis 
in usage, but it is convenient. When a sentence is not significant, 
I call it "nonsensical". 

No ordinary language contains syntactical rules forbidding 
the construction of nonsensical sentences; e.g. the sentence 
"quadruplicity drinks procrastination" is not one that gram 
marians can condemn. Yet it seems clear that it must be 


Ulf ' ^ 



Dossible to construct a language having the following two 
properties : 

(i) Every sentence composed according to the rules of syntax 
Dut of words having meaning is significant ; 

(2) Every significant sentence consists of words having 
neaning and put together according to the rules of syntax. 

It should be observed that meaning of words and significance 
sentences are intertwined except as regards object-words. 
Dther words are defined by means of the significance of the 
simplest sentences in which they can occur. 

But although it should be possible, in a good language, to 
give syntactical rules determining when a sentence is significant, 
't must not be supposed that "significance" is a syntactical con- 

:ept. On the contrary, a non-tautologous sentence is significant 
!n virtue of some relation that it has to certain states of the person 
ising the sentence. These states are "belie vings" and are instances 

of the same belief which is "expressed" by the sentence. In 

defining the relation of the sentence to the belief (which latter is 

in general non-verbal), we have to remember that false sentences 

are significant as well as true ones. And when the relation has been 

defined, we have to show that our syntactical rules of significance 
are such as it justifies. 

The analysis of belief as a state of the believer does not involve 
the concepts "true" and "false"; while we are concerned with 
belief on the subjective side, we need only consider sentences as 
"expressing" states of those who use them. But it is part of the of a sentence in the indicative to "indicate" one or more 
facts which, in general, are not states of the person pronouncing 
the sentence. As soon as we consider this aspect of sentences, we 
become concerned with truth and falsehood, since only true 


sentences succeed in indicating. What sentences "indicate' 
considered in Chapter XV, and from this point onwards we are 
concerned with problems involving "truth" and "falsehood* 

In the analysis of what 



propositional attitudes 




occurrences such as believing, doubting, desiring, etc 



are naturally described 

sentences containing subordinate 

Pll ■ I r 

- Ji' 


■ r4 

V- KC 

:■ '1 ■!' 





■'■- j ■"■. 

y. ■ , 











sentences, e.g. "I think it will rain", we have a complicated 
mixture of empirical and s}aitactical questions. On the face of it, 
the syntactical form of "A believes /' is peculiar in the fact that 
it contains a subordinate sentence * V. The occurrence which 

makes "A believes p' true seems to be a complex containing a 
subordinate complex, and we have to inquire whether there is 
any way of avoiding such an account of belief. 

Propositional attitudes, prima facie^ throw doubt on two 
principles that are assumed by many mathematical logicians, 
namely the principles of extensionality and atomicity. 

The principle of extensionality has two parts : 
. The truth-value of any function of a proposition depends 

only upon the truth-value of the argument, i.e. if p and q are 

boti true or both false, then any sentence containing p remains 
true or false, as the case may be, if q is substituted for p. 

IL The truth-value of any function of a function depends 
only on the extension of the function, i.e. if whenever <t>x is 
true, ^x is true, and vice versa, then any sentence about the 
function ^ remains true or false as the case may be, if ^ is sub- 
stituted for <^. 

Neither of these appears to be true of propositional attitudes . 

man may believe one true proposition without believing 
another; he may believe that some featherless bipeds are not 
men without believing that some men are not men. Thus we 
become involved in an analysis of belief and other propositional 
attitudes in our attempt to decide what looks like a purely logical 

The prindple of atomicity is stated by Wittgenstein as follows 
(Tractatus, 2.0201): **Every statement about complexes can be 
analysed into a statement d>out their constituent parts, and into 
those propositions which completely describe the complexes.'* 
This, if true, implies that in **A believes p'\ p does not occur as 
a unit, but only its constituents occur. 

In the above form, the meaning of the principle of atomicity 
is not very clear. But there is a technical form of the principle, 
not perhaps stricdy equivalent to Wittgenstein's form, but easier 



to discuss, more definite, and therefore (I think) more important. 
In this form, it states that everything we wish to say can be said 
in sentences belonging to the "atomistic hierarchy" which will 
be defined in section C of Chapter XIIL For logic it is important 
to know whether, in this technical form, the principle is true. 
\>JTiat is meant by saying that the principle is "true** is that it is 
possible to construct a language such that (a) every sentence in 
the language is constructed in accordance with the principle, 
and {b) every significant sentence in any language can be trans- 
lated into our constructed language. 

We have thus to discuss the following questions in the following 
order : 

L What is meant by the *' significance" of a sentence, and what 
syntactical rules can we give to determine when a sentence is 
significant ? 

IL Have we any need of "propositions" as opposed to 

"sentences" ? 

A believes p'\ and in 

III. What is the correct analysis of * 
what sense, if any, does "/?" occur in "A believes /?" ? (What is 
said about belief may be extended to other prepositional attitudes.) 

IV. Can we construct an adequate language in which the 


principle of extensionality holds.'* I mean by an * 
language one into which we can translate any significant sentence 

of any language. 

V. Can we construct an adequate language in which the 

principle of atomicity holds } 


\ ' 

Chapter XIII 


A. General 

The question as to what makes a sentence significant is forced 
upon us by various problems* 

There are, in the first place, the recognized rules of syntax 
in ordinary languages. "Socrates is a man" is constructed in 
accordance with these rules, and is significant; but "is a man", 
considered as a complete sentence, violates the rules and is non- 
sensical. (I use "nonsensical" as thecontradictory of "significant". 

The rules of sjmtax in ordinary languages are obviously intended 
to prevent nonsense, . but they fail to achieve their purpose com- 
pletely. As we have already noted, "quadruplicity drinks pro- 
crastination" is nonsense, but violates no rules of English syntax. 
It must clearly be part of our present problem to construct better 
rules of syntax, which shall automatically prevent nonsense. In 
the early stages of our discussion, we are guided by the mere 
feeling as to what is significant, but we hope in the end to arrive 
at something better. 

There is one sense of the word "possibility" which is con- 
nected with our present problem. We may say that whatever is 
asserted by a significant sentence has a certaiin kind of possibility. 
I will define this as "syntactic" possibility. It is perhaps narrower 
than logical possibility, but certainly wider than physical possi- 
bility^ "The moon is made of green cheese" is syntactically 
possible, but not physically. It is difficult to give any indisputable 
instance of a logical possibility which is not syntactically possible; 
perhaps "this is both red and blue" is an instance, and perhaps 
"the sound of a trombone is blue" is an instance. 

I shall not ask, at this stage, what it is that is possible in the 



h r 


case of a sentence which is significant and false. It cannot be the 

for that is actuaL nor can it be "that the sentence is 

true*', for that is merely another false sentence. There is thus a 
problem, but for the present I shall not pursue it. 

The question of "significance'* is difficult and somewhat 
intricate. It will perhaps help to clarify the discussion to state, 

in outline, the conclusion at which I shall arrive, which is as 



An assertion has two sides, subjective and objective. Sub- 
jectively, it "expresses" a state of the speaker, which may be 
called a "belief", which may exist without words, and even in 
animals and infants who do not possess language. Objectively, 
the assertion, if true, "indicates" a fact: if false, it intends to 

, ** ..*»*^, 

, ** *«*«v,. 

"indicate" a fact, but fails to do so. There are some assertions, 
namely those which assert present states of the speaker which he 
notices, in which what is "expressed" and what is "indicated" 
are identical; but in general these two are different. The "signi- 
ficance" of a sentence is what it "expresses". Thus true and false 
sentences are equally significant, but a string of words which 
cannot express any state of the speaker is nonsensical. 

In the following discussion the above theory will gradually 

as, in my opinion, the only one which gives a clear 
solution of the problems that present themselves. 

The question of significance may be brought into connection 
with sentences heard rather than spoken. The hearing of a signi- 
ficant statement has effects dependent upon the nature of the 
statement but not upon its truth or falsehood ; the hearing what 
is recognized as nonsense has no such effects. It is true that what 
is in fact nonsense, may have effects such as only a significant 
statement should have, but in that case the hearer usually imagines 
a signification of which the words are not strictly susceptible. 
Broadly speaking, we may say that a heard statement, interpreted 
by the hearer as significant, is capable of effects of which obvious 
nonsense is incapable. This is one of the points to be borne in 
mind in seeking a definition of "significance". 

Xhe subject of significance has been shown to be more difiicalt 






than it seemed by the paradoxes* It is clear that all the paradoxes 

from the attribution of signilScance to sentences that are 


in fact nonsensical. The paradoxes must be taken account of in 
formulating syntactical rules for the exclusion of nonsense. 

The problem of the law of excluded middle is also connected 
with our present question. It is customary to say that every 
proposition is true or false, but we cannot say that every sentence 
is true or false, since nonsensical sentences are neither. If we are 
to apply the law of excluded middle to sentences, we must first 
know what sentences are significant, since it is only to them that 
the law can apply. Whether it applies to all of them is a question 


attitudes is concluded 

shall consider after the discussion of propositional 

shall first consider the adjective "significant 



and then 

examine the question whether, when a sentence is significant, 
there is something that it "signifies". The word "Caesar'* means 
Caesar; is there anything analogous in regard to sentences.^ 
Technically, if "/'* is a sentence 

can we distinguish between / 



we distinguish between "Caesar" and Caesar 

With these preliminaries 





to detailed 



Sentences are of three sorts: true, false, and nonsensical, 
follows that "false", when applied to sentences, is not synonymous 


"not true", for a 

nonsensical sentence is not true, but is 

also not false. We must therefore, if "/?" is a nonsensical sentence 


distinguish between "/ is false 



tc < 

is true' is false". The 

latter will be true, but not the former. Assuming that "not-/?" 
means "/? is false", we shall have, if/? is nonsensical, "not-(/7 is 

. We shall say that, when 



but we shall not have 


"p" is meaningless, so is 




Thus if "/?" is a phrase concerning which we have not yet 

decided whether it has significance or not, the situation is as 

follows : 

From "/? is true" we can infer 

« » 


and vice versa 


From "jD is false" we can infer "/? is not true", but not vice 









'p is false' is true 


we can infer 

cc c 

p IS txue 




but not vice versa 



(< ( 





we can only infer "/> is true or 


nonsense", but from 
* /? is true**. 

p IS 

" * '" not true' is not true" we can infer 

Let us illustrate by an example. We will start with the sentence 

"this** is a proper name. Let us call this 

this is red'* where 


cc 99 

, Now consider the sentence */? is red". This seems 
obviously nonsense; but if we meant by "/?*' a written or printed 
sentential shape, it would not be, for this might be red. This is 
easy to understand if we accept the distinction between * /?" and 
where "/?*' is a sentence, and^ is the proposition that it signifies; 


for "/?" may be red, but "/? is red" is nonsense. For the moment 
we may take / to be a thought, and * />" the phrase in which the 

thought is expressed. In that case, * jc? is red" is meaningless 

we can distinguish between "/?" and jt>, the whole matter becomes 
clear. Let us give the proper name "P" to the sentential utterance 
"this is red". Then we say that P signifies /?, that p is true, and 
that P signifies a truth. Let us give the name **Q" to the sentential 



is red 


In that case, no 

statement of the form 

signifies j'* is true, and Q signifies neither a truth nor a falsehood 

Assuming still that there is a distinction between ' /?'* and p, I 
prefer to say that "/?'* signifies p rather than that "jo** means /?, 
because "meaning" is better kept for single words. In that case, 
we shall say that a "proposition" (if there is such a thing) is some- 
thing "signified** by some phrase, and that nonsensical phrases 
signify nothing. The problem that remains, in that case, is to 
decide what phrases signify something, and what this something is. 

But all this assumes that we can refute whatever reasons exist 
for denying the distinction between "/>'* and /?, or at least arrive 
at some relevant distinction not affected by those reasons. I shall 
return to this question presendy. 

The distinction between strings of words that signify some- 
thing and strings of words that signify nothing is, in many cases, 
perfectly clear. "Socrates is a man*' signifies something, but "is a 



does not. "Socrates, having drunk the hemlock 






farewell to his friends" signifies something, but "having drunk 
the hemlock, bade farewell to" signifies nothing. In these instances 
there are too few words to make sense, but there may be too 
many. For example, " 'Socrates is a man' is a man" signifies 
nothing. "The law of contradiction is yellow" is a similar kind 
of nonsense. Sometimes there may be doubt, for instance in such 
a case as "the sound of a trombone is blue". The paradoxes arise 
from sentences that seem to signify something, but do not* Of 
these the simplest is "I am lying". This is capable of an infinite 
ntimber of significations, but none of them is quite what we 
should have thought we meant. If we mean "I utter a false pro 
position in the primary language", we are lying, since this is a 
proposition in the secondary language; the argument that 
we are lying, we are speaking the truth, fails, since our false 
statement is of the second order and we said we were uttering a 
false statement of the first order. Similarly if we mean "I utter 
a false proposition of order n". If I try to say "I utter a false 
proposition of the first order, likewise one of the second, of the 



third, fourth , , . ad infinitum^ I shall be asserting simul- 
taneously (if it were possible) an infinite number of propositions, 

of which the ist, 3rd, 5th .. . would be false, the 2nd, 4th, 6th 
. . , true. 

The question whether a form of words signifies anything is 
thus not always easy, but there can be no doubt that some forms 
of words signify something, while others do not, and that among 
those that signify something some signify what is true, while 
others signify what is false. We must therefore find some way of 
defining the difference between strings of words that are nonsense 
and strings of words that signify something ; and in the case of a 
sentence that signifies something, we have to inquire whether the 
something must be different from the sentence, or whether 
significance can be merely adjectival. 

ijfa form of words signifies a proposition, I shall call the pro- 
position the "significance" of the form of words. For the moment 

I assume that there is a proposition which a significant sentence 





Two questions arise: (i) what is meant by the "significance" 
of a form of words ? (2) what syntactical rules can be given as 
to -v^hen a form of words is significant 

"What is meant by the "significance'* of a form of words? 
use the word "significance", here, in a restricted sense; the signi- 
fi^cance in question must be propositional. E.g. "the King of 
England" is a phrase which has meaning in one sense, but does 
not have "significance" in the sense with which I am concerned. 

our present purpose, what the phrase signifies must be 
something true or false. What I am calling "significance" might 
be called "propositional significance", to distinguish it from 

r kinds, but for brevity I shall omit the word "proposi- 

-Al sufficient but not necessary criterion of significance is that. 

perceptual experiences can be imagined, or actually occur, which 
naake us use the phrase (or its contradictory) as an assertion. In 
certain circumstances, we may say, as expressing what we per- 

, "snow is white"; therefore die phrase "snow is white" is 

significant In certain perceptive circumstances we may say snow 
is not black"; therefore the phrase "snow is black" is significant. 
Perhaps this will give us a hint as to what, in general, is "signified" 
by a phrase which has significance. 

When I say "snow is white", what makes my statement true 
is one thing and what I express is another. What makes my state- 
ment true is a fact of physics, concerned with snow, but I am 
expressing a state of mind, namely a certain belief — or, to allow 

lying, a desire that others should have a certain belief. We 
omit this complication, and assume that, in asserting the 

ds, I express a belief. But I am not asserting that I have a 

belief; I am asserting the object of the belief. Is there an object 
of the belief, which is what is asserted by the phrase "snow is 
wliite".^ Certain experiences cause us to believe that snow is 
^?^^lite; if this belief has an object, we may say that I express th^ 

that I believe something (namely, that snow is white) by 

_ this object. I do not assert that I believe the object 
that would be a diflferent assertion, which might be true even if 



snow were black. Our. problem is : is there something, and if so 
what, that I believe when I believe that snow is white ? 

Again: what are you asking if you say **is snow white** ? Let 
us suppose that you grew up in Ethiopia, but that, as a result of 
an air raid, you were captured, blindfolded, and transported to 
the Arctic Circle, where you became acquainted with the touch 


taste and smell of snow, and learnt that "snow 


was the 

name of the substance thus manifested to three of your senses. 
You might then ask "is snoy/ white ?** You would not be asking 
about the word "snow" and the word "white**, but about percepts. 
You might mean : do those who are not blindfolded, when they 

have the sensations of touch and smell that I have learnt to 
associate with the word "snow**, see whiteness } But even this is 
still too verbal. If you are, at the moment, touching and smelling 
snow, you may mean "is this usually associated with whiteness ?" 
And if you are imagining whiteness, the thought in your mind 

may be 


tUs usually associated with thatV^ where this is the 

tactual and olfactory percept, and that is the image of whiteness. 

must not be interpreted as the image itself; it must 



rather mean a percept like the image. At this point, however, it 
becomes very dijfficult to be clear; for the image seems to **mean" 
a percept in the same sort of way in which a word does. 

It is obvious that, if beliefs have objects, what I believe when 
I believe that snow is white is the same as what I doubt when I 

ask "is snow white •^** This, whatever it is, is, on this hypothesis, 
the significance of the sentence "snow is white**. If the significance 
of the sentence is true, that is in virtue of occurrences which are 

neither words nor images ; if it is hmwn to be true, these occur- 
rences must be or have been percepts. The same holds, mutatis 
mutandis^ if it is false. Truth and falsehood depend upon a 
relation between the significance of the sentence and something 
which is neither words nor images (except when the sentence 
is about words or images) 

of a 
sentence, we shall say that it is this significance that is to be called 

If we can decide what is meant by the "significance 

a "proposition**, and that is either true or false. A sentence may 


h 1 



signify a truth, or signify a falsehood, or signify nothing; but 
if a sentence signifies anything, then what it signifies must be 
true or false. 

of a 
sentence, let us contrast a significant sentence with one that is 

To try to discover what is meant by the '^significance*' 

not significant. Take "Socrates drinks the hemlock" and "quad 

ruplicity drinks procrastination". Of these the former logically 
can be, and once was, a judgment of perception; when it is not 
a judgment of perception, it is capable of calling up a complex 
image which has the same significance as, or, perhaps, is the 

of, the 


phrase. But we cannot form an image of 
quadruplicity drinking. When we try to do so, we merely imagine 

Quadruplidty". Let us ask 


man whom, for 

fun, we call 


ourselves: how can such a word as "quadmplidty" refer to 
anything experienced.^ Suppose you are being subjected to 
military drill, and constantly hearing the order "form fours". 
You may, if you are fond of abstract words, reflect "quadruplicity 

IS prominent m 





in drill, there are many 

occurrences in the verbal description of which it is natural to 

use the word Your' ". We may define "quadmplicity" as "that 
property of a propositional function which consists in being tme 
for exactly four values of the variable". Thus we have to ask: 
how do we know that it is nonsense to suppose that a property 

of a propositional function can drink.'* It is difiicult, but not 

very diflScult, to constmct rules of syntax which, given the 
meanings of the separate words, shall insure that every combina- 
tion of words which obeys the mles shall be significant, and every 
significant combination of words shall obey the rules. This work 
has, in fact, been done by the logicians, not perhaps completely 


but with a fair degree of adequacy. The trouble is that, in this 
work, they have, at least in part, been guided by feeling, like 
the plain man. We cannot rest satisfied with our rules of signi- 
ficance unless we can see some reason for them, and this requires 
that we should decide what a form of words signifies when it is 


We msiy put the question in the form: "what do we believe 

177 . 


when we believe something?" Let us take an illustration. In some 
quarries, there is a big blasting operation every day at twelve 
o'clock. The signal to clear out of the way is given by a horn; 
there may also be men with red flags on the neighbouring roads 
and paths. If you ask them why they are there, they will say 
"because there is going to be an explosion". The operatives who 
understand the horn, the neighbours who understand the red 
flag, and the passing stranger who needs words, all, in the end, 
believe the same proposition, namely that expressed by the words 
"there is going to be an explosion". But probably only the passing 
stranger and his informant put this belief into words ; for the 
others, the horn and the red flag serve the purposes of language 

and produce the appropriate actions without the need of any 
verbal intermediary. 

The horn and the flag may count as language, since their 
purpose is to convey information. But an approaching shell 
would convey very similar information without being language, 
since its purpose would not be to instruct. The shell the horn' 

, t-.*w **vr**i. 

and die flag may all alike cause belief without causing words. 
When a number of people all believe that there is going to be 

an explosion, what have they in conunon.^ A certain state of 

tension, which will be discharged when the explosion occurs, 
but, if their belief was false, will continue for some time, and 
then give place to surprise. The state of tension may be called 
"expectation"; but the difiiculty arises as regards the connection 
of diis (a) with the explosion or its absence, (b) with something 
which, in order to be vague, we will call the "idea" of the 
explosion. It is obvious that to expect an explosion is one thing, 
and to expect (say) the arrival of a train is another. They have in 
common the feeUng of expectation, but they differ as to the 
event which will change this feeling into acquiescence or surprise. 
This feeling, therefore, cannot be the only thing that constitutes 
the state of die person who is expecting something, since, if it 
were, any event would satisfy his expectation, whereas, in fact 

only an event of a certain kind will do so. Perhaps, however, 
the whole thing could be explained physiologically } Everybody 



who is expecting a flash-light has sensations in the eyes, and the 
expectation of a loud noise involves something similar in con- 
nection with the ears. It might be said, therefore, that expectation 
of a sensible phenomenon consists in a state of receptivity of the 
appropriate sense-organs. But there are feelings connected with 
such a state of receptivity, and these feelings may be taken as 
constituting the mental part of an expectation. 

It would seem, therefore, that what is in common among a 
number of people who all believe what is expressed by the 
words "there is about to be a bang'* is a state of tension connected 
with the appropriate sense-organs, a physiological condition of 
those organs, and the feelings which accompany such a condition. 
We can say the same of "there is about to be a flash" or "there 
is about to be the smell of a room full of ferrets". But these are 
very emphatic occurrences, and are all in the immediate future. 
When I believe something less exciting — that tomorrow's Times 
will contain a weather forecast, or that Caesar crossed the 

Rubicon — ^I cannot observe any such occurrences in myself 
you were to tell me "you will be murdered in a minute", perhaps 
my hair would stand on end ; but when you tell me that Caesar 
was murdered on the Ides of March, my hair remains no more 
untidy than before, in spite of the fact that I quite believe what 

you say. 

This difference, however, is probably only one of degree 

unless the belief involved is merely verbal. When I speak of a 

belief being "merely verbal", I do not mean only that it. is ex- 
pressed in words, but that what the words signify is not in the 
mind of the believer, who is merely thinking that the words are 
correct. We know that "William the Conqueror 1066" is correct, 
but we do not often stop to think what this phrase signifies 

In such a case we are not believing "/>", but believing 
signifies a truth". The beliefs of educated people are largely of 
this kind. But the beliefs that primarily concern us are those that 
are not purely verbal. For until we have dealt with them we 
cannot explain what is meant by "signifying a truth". 

When you are expecting an explosion, your body is in a certain 



State, and your mind in a corresponding state. This may bring 
the word "explosion" into your mind, and the word "explosion**, 
at any rate with a small verbal addition, may cause the state of 

expectation. If you are told "there has just been an explosion 
and you vividly believe what you are told, your state of body and 
mind will become to some extent like what it would have been if 
you had heard the explosion, though less intense. Imagination, 
if sufficiently powerful, can have physical eifects analogous to 
those of perception; this is especially the case when -what is 
imagined is believed to have taken place. Words, without 

images, may, through association, have these effects. And wher 
ever there are such physical effects there are concomitant mental 

Perhaps we can now explain the "significance" of a sentence 
as follows. First : some sentences signify observed facts ; how this 
happens, we have already considered. Second: some observed 
facts are beliefs. A belief need not involve any words at all in the 
beiliever, but it is always possible (given a suitable vocabulary) to 
find a sentence signifying the perceived fact that I have such- 
and-such a belief. If this sentence begins "I believe that", what 

follows the word 



is a sentence signifying a proposition 


and the proposition is said to be what I am believing. Exactly 
similar remarks apply to doubt, desire, etc. 


According to this view, if /? is a proposition, "I believe p", 

I doubt p", "I desire p 




may signify observed facts 



i< 99 

it may happen that "jp" signifies an observed fact. In this last case, 

can stand alone and be significant of a percept, but otherwise 

alone does 

« 99 

CC 99 

alone signifies nothing perceived. Perhaps, 
signify something; perhaps, as we suggested earlier, it signifies a 
subordinate complex which is a constituent of a prepositional 
attitude. In that case, however, we shall have to explain why such 

complexes never occur except as constituents of propositional 

The above theory has difficulties. One difficulty is to explain 
the relation of/ to the fact when p is true. Suppose, for example 
I see the letters "A B** in that order, and I judge "A is to the left 




of B'\ I am, in that case, believing a proposition p which has a 
certain relation to a fact. We are supposing that p is not verbal, 
but is something non-verbal, which is signified by the words "A 
is to the left of B'\ but is not the fact in virtue of which these 


words express a truth. It might be urged that we have to assign 
to words two different uses, one when we assert /?, and another 
when we assert that we believe/?. For when we assert p (assuming 
p to be a judgment of perception), the words of "/", it may be 
said, denote objects, whereas, when we assert that we believe p 
the words have to have some mental meaning. According to this 
view, when I say **Socrates is Greek", Socrates is involved, but 
when I say "I believe that Socrates is Greek", only my idea of 
Socrates is involved. This seems hardly credible. 

I think this objection is invalid. Suppose I see a red circle and 




\ In using words, I have passed away from the 
percept; if, instead of words, I use images, they, like the words, 
mean the percept, but are something different from it. When I 
say "this is red", or when I have a red image with a yes-feeling, 
I have a belief; if I afterwards say **I believe that was red", the 
words and images involved may be just the same as they were 
when I made a judgment of perception. Seeing is not believing, 
and a judgment of perception is not a perception. 

Our present suggestion is that a sentence "/>" is significant if 

believe that 



doubt that p' or etc 


can describe a 


perceived fact in which words need not occur. There are 
culties: "can describe" is vague; "words need not occur" needs 
elucidation. Nevertheless, perhaps something could be made of 

our suggestion. 

In the first place, we must elucidate the statement that words 
need not occur. Sometimes they occur, sometimes they do not; 
in propositions which are complicated, they are practically indis- 
pensable, though with greater mental powers we might be able 
to do without them. The other question, as to what is meant by 
"can describe a perceived fact", is more difficult. We obviously 
do not wish to exclude all sentences which have not in fact entered 
into propositional attitudes. We want to find a characteristic of 



sentences which makes us feel that it is possible to believe or doubt 
them, and until this is found our problem is not solved. 

We might try to define significance in a more linguistic fashion. 
We first divide words into categories, having affinities with the 
parts of speech. We then say : given any judgment of perception 
(which may be of the form "I believe /?"), any word may be 
replaced by another word belonging to the same category without 
making the sentence lose significance. And we allow the formation 
of molecular and generalized propositions by the methods already 
considered. We shall then say that the assemblage of sentences 
so obtained is the class of significant sentences. But why } I do 
not doubt that some linguistic definition of the class of significant 
sentences — either the above or another — ^is possible; but we 
cannot rest content until we have found some reason for our 
linguistic rules. 

If a reason for our linguistic rules is to be found, it must consist 
of properties of complexes which are in some way related to the 
rules. In such a proposition as "A is to the left of B", when this 
is a judgment of perception, we are analysing a complex percept. 
It seems that, in any phrase expressing such an analysis, there 

must be at least one relation- word. I do not believe that this is 

only a property of language; I believe that the complex has a 
corresponding constituent which is a relation. I think that when 
we say that a phrase is significant, we mean that a complex 
described by the phrase is "possible"; and when we say that a 
complex described by a phrase is "possible", we mean that there 
is a complex described by a phrase obtained from the given 

phrase by substituting for one or more of its words other words 
belonging to the same categories. Thus if "A" and "B" are names 
of men, ' * A killed B' * is possible because Brutus killed Caesar ; 
and if "R" is the name of a relation of the same category as 
killing, "A has the relation R to B" is possible for the same reason. 
At this point we touch on the relations between linguistics and 
metaphysics. I shall deal with this matter in a later chapter. 

Reverting now to what is meant by the "significance" of a 

sentence, we shall say that, in the case of a sentence of atomic 







form the significance is a state of the believer, or rather a set of 
sucH states having certain similarities. A possible form of such a 

IS a 

complex image, or rather a whole set of similar complex 
images. Im^g^^ form a language, but the language differs from 

that of words in the fact that it does not contain any nonsense. 
To extend die definition of "significance" beyond atomic sen 


is obviously only a question of logic. 

I have been assuming that, when a sentence is significant, 
there is something that it signifies. Since a significant sentence 
m<z^ be false, it is clear that the signification of a sentence cannot 
be the fact that makes it true (or false). It must therefore be 

soinething in the person who believes the sentence, not in the 
object to which the sentence refers. Images are naturally sug- 

Images "mean" in much the same way as words do, but 
they have the advantage that there are no complex images corre- 
sponding to nonsensical sentences. Actual pictures have the same 
merit. lean make a picture of Brutus killing Caesar, or, if I choose, 
of Caesar killing Brutus, but I cannot make a picture, either real 

or ima 

ined, of quadruplicity killing procrastination. The syn 

rules for obtaining other significant sentences from judg- 
ments of perception are really, according to this theory, psy- 
chological laws as to what can be imagined. 

above theory is, I think, a possible one. It is, however, 
in certain respects repellent. The use of images is to be avoided 
whenever possible ; and Occam's razor makes us wish, if we can, 
to avoid propositions as something distinct from sentences. Let 
us, .therefore, attempt to frame a theory in which significance is 

merely an adjective of sentences. 

most hopeful suggestion is to distinguish significant from 

sentences by their causal properties. We can dis 
tingxiish true from false sentences (where judgments of perception 
are concerned) by the causes of their being uttered ; but since we 

dealing with a problem in which true and false sentences 
level we shall have to consider rather the effects in the 

are on a -.^,^*, 

than the causes in the speaker. 
Ivlany heard sentences have no observable effect upon the 






hearer's actions, but they are always capable of having an effect 
in suitable circumstances. "Caesar is dead" has very little effect 
upon us now, but had great effects at the. time. Nonsensical 
sentences, recognized as such, do not promote any action relative 
to what their constituent words mean; the most they can produce 
is a request to the speaker to hold his tongue. They are therefore, 
it would seem, causally distinguishable from significant sentences. 
There are, however, some difficulties. Lamb, in an altercation 
with a Billingsgate fish-wife, called her a she-parallelogram, and 
produced a greater eflFect than he could have done by any more 
significant abuse; this was because she did not know his sentence 
to be nonsense. Many religious people are much affected by such 

sentences as 


is one", which are 

syntactically faulty, and 

must be regarded by the logician as strictly meaningless. (The 
correct phrase would be "There is only one God".) Thus the 
hearer in relation to whom significance is to be defined must be a 
logically trained listener. This removes us from the sphere of 
psychological observation, since it sets up a standard by which 
one hearer is logically preferable to another. What makes him 
preferable must be something in logic, not something definable 
in terms of behaviour. 

In Mind for October 1939 there is an interesting article by 

Kaplan and Copilowish, on "Must there be propositions.^" They 

reply in the negative. I propose to re-state and then examine their 

They introduce the term "implicit behaviour" in a very wide 
sense, as whatever happens to or "in" an organism when it uses 
signs. They leave open the question whether implicit behaviour 

is to be described behaviouristically or in images 

behaviour occasioned by a sign-vehicle is called an 




tion". Associated with each sign-vehicle there is a law of inter 
pretation^ stating the kind of implicit behaviour that it occasions. 
A sign is a class of sign-vehicles all having one and the same law 
of interpretation; this law is called the interpretant of the sign. 
An interpretation of a sign-vehicle is correct if the law describing 
the interpretation has been previously set up as standard for such 






" \ 


sign-vehicles. We say O understands 2l sign when O correctly 

interprets a member of it under certain conditions. O believes 

a sign-vehicle when O has a correct interpretation of it together 

with an "attitude of affirmation" (provisionally undefined). 
Believing a sign is a disposition. We are told: "an organism may 
be said to have a belief even where signs are not involved. This 
is the case where the organism has an implicit behaviour of such 
a kind that, had it been occasioned by a sign-vehicle, it would 
have constituted a belief of that sign-vehicle". 

We now come to the definition of "appropriate": the implicit 
behaviour of an organism O is appropriate to a situation S if it is 
caused by S and O recognizes S. (The word "recognize", which 
occurs here, is not defined in the article, and has not been dis- 
cussed previously.) Interpretation being a kind of implicit 
behaviour, we say that an interpretation of a sign is appropriate 
to S if it would be appropriate to S if S were present and recog- 
nized. Hence follows a definition of "true": 

"A sentential sign is true if and only if there exists a situation 
of such a kind that a correct interpretation of any sign-vehicle 
of the sign is appropriate to the situation." 

Before we can successfully examine the adequacy of this 

: the word 

"sign", or rather "sign- vehicle", is not defined- In order to define 
it, I should say, we must begin near the end of the above set of 
definitions. One event only becomes a sign-vehicle of another in 
virtue of similarity in its eflFects. I should say: "a class of events 
S is, for an organism O, a si^n of another class of events E, wh^n 

theory, there are some necessary preliminaries. First 


as a result of acquired habit, the effects of a member of S on. O 
are (in certain respects and with certain limitations) those which 
a member of E had before the habit in question was acquired". 
This definition is incomplete so long as the above-mentioned 
respects and limitations are not specified; but this is not an 
objection of principle. Further : I am not sure that it is right to 
limit signs to acquired habits; perhaps unconditioned reflexes 
should also be admitted. Since, however, our principal concern 
is with language, it is convenient to exclude them. 



Thje difficulty of this subject comes largely from the inter- 
mingling of scientific and normative terms. Thus in Kaplan and 
Copilowish's series of definitions we find the words "correct" 
and "appropriate". Each of these is defined in a way which is 
not normative, at least in intention. Let us look at the definitions 
more closely. 

"An interpretation of a sign- vehicle is correct if the law which 
describes that interpretation has previously been taken as standard 
for sign-vehicles of that kind (i.e. of that sound or shape)". The 
word "standard" is vague. Let us make it precise: let us say that 
the "correct" interpretation is that given by the Oxford Die-- 
mnary^ supplemented (under the influence of Semiotics) by an 
eminent physiologist's description of his reactions to such words 
as have only an ostensive definition. The physiologist having 
been selected and his work completed, our definition of "correct" 
is now freed from all ethical taint. But the results will be odd. 
Suppose a man who thinks that "cat" means the kind of animal 
that other people call "dog". If he sees a Great Dane and says 
"there is a cat", he is believing a true proposition, but uttering 
an incorrect one. It would seem, therefore, that "correct" cannot 

3 ^*-w*^*N^*v-, 




be used in defining "true", since "correct" is a social concept 
but "true" is not. 

Perhaps this difficulty could be overcome. When our man says 
there is a cat", what would ordinarily be called his "thought 
is true, but the "thought" that he causes in his hearer is untrue. 
His implicit behaviour will be appropriate, in the sense that he 
will (for example) expect the animal to bark and not mew, but 
the hearer's implicit behaviour will, in the same sense, be in 
appropriate. The speaker and the hearer use different languages 
(at least so far as the words "cat" and "dog" are concerned). I 
think that, in fundamental discussions of language, its social 
aspect should be ignored, and a man should always be supposed 
to be speaking to himself— or, what comes to the same thing, to 
man whose language is precisely identical with his own. This 

eliminates the concept of "correctness". What remains — if a 

man is to be able to interpret notes written by himself on previous 

1 86 


occasions — ^is constancy in his own use of words : we must 
suppose that he uses the same language today as he used yester- 
day, in fact, the whole residuum of what was to have been done 
by the concept of "correctness" is this: speaker and hearer (or 
writer and reader) must use the same language, i.e. have the same 
interpretative habits. 

I come now to the term "appropriate". Here I find less occasion 
for criticism, except that, in my opinion, the definition of "appro- 
priate" can be absorbed into the definition of "sign- vehicle". 

s is, for O, a sign- vehicle of a class of events E, that means 
that O's reactions to s are "appropriate" to E, i.e. are (with suitable 

limitations) identical with the reactions which O makes to a 
member of E on occasions when such a member is present. Let 
us now try to re-state the above definition of "true" without 
using the concept of "correct". We might say: "a sentential sign 

present to an organism O is true when, as sign^ it promotes 
behaviour which would have been promoted by a situation that 
exists, if this situation had been present to the organism". 

I say "as sign", because we have to exclude behaviour which 
the sign promotes on its own account — e.g. it may be so loud as 
to cause the hearer to stop his ears. Such behaviour is irrelevant. 
I say "if this situation had been present to the organism", meaning 
not to state that it is not present, but only to allow for the possi- 
bility of its not being present. If it is present, we cannot dis- 
tinguish behaviour caused by the sign from behaviour caused 

by what it signifies. 

There is a more or less formal emendation which is required 
in the above definition of "true". This has to do with the phrase 
"behaviour which would have been promoted by a situation, if 
this situation had been present to the organism". This definition 
will not have the intended significance in the case of a situation 
which has never, in fact, been present to the organism. Formally, 
since a false proposition implies every other proposition, the 
condition is satisfied, in this case, by any sentential sign; We 
must therefore amend our definition by saying that, on various 
occasions, situations sufficiently similar to the given situation 



have, in fact, promoted behaviour sufficiently similar to the 
behaviour now promoted by the sign. The degree of similarity 
required cannot be defined in general terms, and is essentially 
subject to a certain degree of vagueness. Moreover the "situa- 
tion** and the "behaviour" involved must both be generic, not 
particular, since it is involved in the emended definition that 

each can occur more than once, 

There is one grave objection to the above definition, and that 
is that it considers sentences exclusively from the standpoint of 
the hearer to the exclusion of that of the speaker. The most 
obvious example of truth is an exclamation caused by some 
feature of the environment, such as "fire!" or "murder!" And 

it is by means of such exclamations on the part of elders that 

children's language habits are acquired. 

. Another objection is that, whenever the situation verifying a 
sentence is not present to the hearer, the truth of the sentence 
must be known only by subsequent inference. The premisses of 
such inference must be known by the simultaneous presence of 
the sentence and what it signifies; this knowledge must therefore 
exemplify the most primitive kind of truth, from which other 
kinds are derivative. 

But as to the main question, namely "must there be proposi- 
tions.?" I should say that the "implicit behaviour" assumed by 
Kaplan and Copilowish is exactly what I mean by "proposition*' 
If you say to an Englishman "there's a cat", to a Frenchman 
"voila un chat", to a German "da ist eine Katze", and to an 
Italian "ecco un gatto", their implicit behaviours will be the same; 
this is what I mean by saying that they are all believing the same 
proposition, though they are believing quite dijGFerent sentences. 
Moreover they can believe the proposition without using words; 
I should say that a dog is believing it when he is excited by the 
smell of a cat* It is the capacity of sentences to promote this kind 
of "implicit behaviour" that makes them important. A sentence 
is significant to the hearer when it promotes this kind of implicit 
behaviour, and to the speaker when it is promoted by it. Precise 
syntactical rules as to what sentences are significant are not psy- 



chologically true ; they are analogous to rules of etiquette. When 
Lamb called the fish-wife a she-parallelogram, the sentence was 

to her significant, and meant "y^^ ^^^ ^^ abominable female 
monster". What can be said, apart from etiquette, in favour of 
such syntactical rules as the logician naturally suggests, is this: 
a language obeying these rules has, for those who understand 
it, the merit that every sentence expresses a proposition, and every 
proposition can be expressed by a sentence (provided the voca- 
bulary is adequate). It has also the merit of a more precise and 
intimate relation between sentences and what they signify than 
exists in ordinary spoken languages. 

conclude, from this long discussion, that it is necessary to 
distinguish propositions from sentences, but that propositions 
need not be indefinable. They are to be defined as psychological 
occurrences of certain sorts — complex images, expectations, etc. 
Such occurrences are "expressed" by sentences, but the sen- 
tences "assert" something else. When two sentences have the 
same meaning, that is because they express the same proposition. 
Words are not essential to propositions. The exact psychological 
definition of propositions is irrelevant to logic and theory of 
knowledge; the only thing essential to our inquiries is that sen- 
tences signify something other than themselves, which can be 
the same when the sentences differ. That this something must be 
psychological (or physiological) is made evident by the fact that 
propositions can be false. 

B. Psychological Analysis of Significance 

We have considered already the psychological character of 
the meanings of single words, when diey are object-words. The 
meaning of a single word is defined by the situations that cause 
it to be used and the effects that result from hearing it. The 
significance of a sentence can be similarly defined; in fact, an 
object-word is a sentence when used in an exclamatory manner. 
So long as we confine ourselves to these generalities there is no 
problem as to the significance of sentences. The problems arise 



when we attempt to explain in psychological terms the relation 
between the significance of a sentence and the meanings of its 
constituent words. To the logician, the significance is definable 
in terms of the meanings of the words and the rules of syntax. 
But psychologically the sentence is a causal unit, and its effect 
does not seem to be compounded of separate effects of separate 
words. Can we say that the effect of "that is not cheese" is com- 
pounded of the effect of "not'* and the effect of "cheese".^ 
we are to say this, we shall need a much more psychological 
theory of logical words than is customary, but I do not consider 
this a decisive argument. 
The syntactical theory of significance — especially when con 

nected with an artificial logical language — ^is a branch of ethics: 
it says "logically well-behaved people will attach significance to 
sentences of the following kinds*'. But there is also a purely psy- 
chological theory of significance. In this theory a spoken sentence 
is "significant" if its causes are of a certain kind, and a heard 
sentence is "significant" if its effects are of a certain kind. The 

psychological theory of significance consists in defining these 

"Belief", we decided, is a certain condition of mind and body, 
not essentially involving words. A person A may be in a condition 
which is described in the words "A believes that there is about to 
be a loud bang". When A is in this condition, it may cause him 
to use the words "there is about to be a loud bang". A sentence 

is significant when there can be a state of mind and body 
described in the words "A believes/?". Hearing the sentence "/' 
is one -possible cause of the state that consists in believing 
A heard sentence is significant when it can be such a cause. 

In the above we have two different definitions of "significance". 
One is relative to the linguistic habits of a person who says "A 
believes/?", the other to those of a person who hears A uttering/?. 

« >9 

u >» 

CC »9 

A man who is in a state of belief may utter a sentence 
with the intention of expressing his belief, but a hearer, with 
other linguistic habits, may consider the expression inaccurate. 
A man A may say "the moon looks as large as a soup-plate"; 

190 , 


B itiay say, "no, only as large as a dollar"; C may say "both your 

are incomplete; you must specify the distance of the 



soup-plate or dollar from the eye". What does C mean by "must 
He means that the sentences of A and B, though apparently 
inconsistent, are not so really, since neither describes a definite 
state of affairs. 

Every object-word has two uses, corresponding to Hume's 

irnpression" and "idea". When direcdy caused by a sensible 

occurrence, the word, in the speaker, applies to an impression; 

when heard, or used in narrative, it does not apply to an im 


pression,- but it is still a word, not a mere noise; it still "means" 
something, and what it "means" may be called an "idea". The 
same distinction applies to sentences: a spoken sentence may 
describe an impression, but a heard sentence does not. "Im- 
pression" and "idea" must be very closely related, since other- 
wise it would be impossible to give information: in some sense, 
what the hearer understands is what the speaker expressed.* 

assume that there is a certain state of a person A which can 
be described in the words "A believes that there is about to be 
a loud bang", and that this state need not involve words in A. 
Btxt it must be possible to describe A's state quite differently, 
by means of certain tensions and auricular stimulations. I shall 
say * * A believes /?" if A is in a condition which, if he shares my 
linguistic habits, and sees occasion to speak, will cause him to 


utter the sentence "/?". 

The matter seems simpler when A has the sentence "/" in 

<( 99 

his mind. But this is a mistake, A may have the sentence 
in his mind, and proceed to say "I believe /?", or simply to assert 

but it does not follow that he believes p. What he must be 
believing is " */?' is true". He may be quite unaware of what "/?" 

mieans. E.g. the devout but uneducated believer who hears the 
Apostles' Creed in Greek, or the school-child who, to please the 

says ''and is a conjunction". 
X-et us try to enumerate the various uses of "^". Take the 

■" This is only roughly true. Its limitations are considered in Chapters XV, 

KVI. and XVII 




sentence "there is a red light", which we will call "p". You are, 
we will suppose, sitting beside a careless driver. You utter the 
sentence because you see a red light; this may be called the 
exclamatory use of 'y\ Here * /?" is directly caused by a sensible 
fact, which it "indicates", and by which it is "verified**. But how 
about the driver who hears your exclamation? He acts exactly 
as he would have done if he had seen the red light; there is in 
him a conditioned reflex which leads him to respond to the words 
"red light" as he responds to the sight of a red light* This is 
what we mean when we say that he "understands" the words. 

So far, we have no need of "ideas". You react to a visual 
stimulus, and the driver to an auditory stimulus; his reaction, like 
yours, is to a present sensible fact. 

But now suppose that when you see the red light you hold 
your tongue, and a moment later remark "it is fortunate there 
was no policeman there, because you ran past a red light", to 
which the driver replies "I don*t believe you". Now "/?" shall 
be "there was a red light". You assert /?, and the driver says he 
does not believe p. 

In this case, the need for "ideas" seems fairly evident. Neither 

you nor the driver is concerned with words : you are not saying 
"the words 'there was a red light' express a truth", nor is he 
denying this. Both are speaking about what the words "mean*' 

So far as you are concerned, we could perhaps be content with 
the analogy of the automatic machine which first says "this is a 
penny" and later "that was a penny". The man who has just 
seen a red light which he no longer sees is, no doubt, in a different 
state from ribat of a man who has seen no red light; tliis state 
may cause the use of the words "there was a red light". As for 
the driver, we may suppose in him a state (involving motor 
impulses) induced by the heard words "there was a red light", 
combined with inhibitory impulses such as are expressed by the 
word "disbelief". So long as we do not introduce "ideas", this 
is not sufl5ciently specific. The motor impulses in the driver will 
be just the same if you say "you nearly ran over a dog"^ but 

his state will not be the same. Your words cause in him the 









of there having been a red light, and he meets this 

thouffht with disbelief. It is unnecessary for us to decide what the 

' consists of, and how it is to be apportioned between 



psychology and physiology, but it seems that we must admit it 

ixiany obviously different beliefs may be indistinguishable 

in. their motor effects. 

Thus the psychological theory of significance to which we 
have been led is as follows. There are states which may be called 

of **believing"; these states do not essentially involve 
w^ords. Two states of believing may be so related that we call 
them instances of the same belief. In a man with suitable language- 
one of the states which is an instance of a given belief is 
which he utters a certain sentence. When the utterance 
of a certain sentence is an instance of a certain belief, the sentence 

id to "express" the belief. A spoken sentence is "significant'* 

■* . .1 i 1 t« r .1 . •. C6 99 A 1 J 




is a possible belief that it "expresses 


sentence "S" may be believed or rejected or doubted. If believed 


hearer's belief is "expressed" by the same sentence 




the hearer's disbelief is "expressed 

the sentence 




; if doubted, by "perhaps S 


A heard sentence 




significant if it can cause any of the three kinds of states 
pressed" by "S", "not-S", and "perhaps S". "When we say simply 
that **S" is significant, we mean that it has this latter kind of 


This whole theory is completely independent of any con 

sidieration of truth and falsehood. 

There is one important respect in which the above theory is 


in common m 

^ it has not decided what two states must have 

order to be instances of the same belief. When 

verbal habits are sufficiently developed, we may say that two 

instances of the same belief if they can be expressed 

t>y the same sentence 


the only definition is causal 

two states are instances of the same belief when they cause the 

behaviour- (This will, in those who possess language 

include the behaviour that consists in uttering a certain sentence.) 

ana not quite satisfied that this causal definition is adequate. 




but, having no better alternative to offer, I shall tentatively 
accept it. 

C. Syntax and Significance* 

In the present section, I propose to consider the possibility 
of constructing a logical language in which the psychological 
conditions of significance, considered in the previous section, are 
translated into precise syntactical rules. 

Starting from a vocabulary derived from perception, and from 

sentences expressing judgments of perception, I shall give a 
definition of an assemblage of significant sentences defined 
their syntactical relation to the initial vocabulary and to judgments 
of perception. When this assemblage has been defined, we can 
consider whether, in an adequate language, it can contain 
significant sentences and no others. 

The initial object-vocabulary consists of names, predicates, 
and relations, all having ostensive definitions. In theory, rela- 
tions may have any finite number of terms; we need not inquire 
what is the greatest number of terms in any sentence expressing 
a relational fact that we actually perceive. AH the words needed 
in the object-vocabulary have ostensive definitions; words 
having dictionary definitions are theoretically superfluous. The 
object-vocabulary is liable to be extended at any moment as a 
result of new experience — e.g. the first time you eat sharks* fins 
you may give a name to the flavour. 

Sentences describing experiences, such as we considered in 
Chapter III, are frequently, though perhaps not always, composed 
of a single relation or predicate together with a suitable number 
of names. Such sentences express "judgments of perception 
They form the basis from which our syntactical construction 


Let Rr,(a^,a2,cu 

be a sentence expressing a judg- 

ment of perception, containing one ;z-adic relation R„ and 
names a^jOz^a^ . . . a„. We then lay down the principle 

* The reader may with advantage omit this section if he is not interested 
mathematical logic. 




substitution : the sentence remains significant if any or all of the 

names are replaced by any other names, and R„ is replaced by 
any other «-adic relation. We thus obtain from judgments of 
perception a certain collection of significant sentences, which we 

call atomic sentences. 

It might be objected that this principle will allow the con- 
struction of nonsensical sentences such as "the sound of a trom- 
bone is blue". With my theory of names, this would assert the 
identity of two objects having different names. This, I should 

say, is not nonsense, but false. I should include among judgments 

perception such sentences as "red is different from blue": 

similarly, if s is the name of the quality of the sound of a 
trombone, "^ is different from blue" can be a judgment of 

It is of course possible, since we are dealing with an arti- 
ficial language, to supply a conventional significance to a sentence 
which has no natural significance, provided we can avoid the risk 
of contradiction. Sentences which have no natural significance 
are obviously not naturally true ; therefore we can supply a false 
significance, such as "this buttercup is blue", for every sentence 
(not containing the word "not") that we wish to include but 
that does not naturally have any significance. Where atomic 
sentences are concerned there is no risk of contradiction ; there- 
fore, if the principle of substitution were otherwise doubtful, its 
validity could be secured by a convention. There is accordingly 
no reason for rejecting it. 

The second principle in the formation of sentences may be 
called combination. A given sentence can be negated; two given 
sentences can be combined by "or", "and", "if-then", "if-then 
not", and so on. Such sentences are called "molecular" if they 
result from a combination of atomic sentences, either directly 
or by any number of finite operations. The truth or falsehood of 

a molecular sentence depends only upon that of its "atoms 


All molecular sentences can be defined in terms of one opera 

tion. If "/?" and "y" are any two sentences "/? | 9" (read 


stroke-y") is to mean "/? and q are not both true", or "/? and 



are incompatible". We can then define "not-/?" as "/ | p\ i.e 

, 1.6 

"/? is incompatible with /?"; "/> or j" as 

''not-/ is incompatible with not-/'; "/? and q' as "(/^ 

i.e. */> and §^ are not incompatible". Starting from atomic pro 


positions, and using the principle that any two sentences can be 
combined by the "stroke" to form a new sentence, we obtain 
the assemblage of "molecular propositions". All this is familiar 
to logicians as the logic of truth-functions. 

The next operation is generalisation. Given any sentence con- 

taining either a name "a" or a word "R" denoting a relation or 
predicate, we can construct a new sentence in two ways. In the 
case of a name "a", we may say that all sentences which result 
from the substitution of another name in place of "a" are true, 
or we may say that at least one such sentence is true. (I must 
repeat that I am not concerned with inferring true sentences, but 
only with constructing sentences syntactically, without regard 
to their truth or falsehood.) For example, from "Socrates is a 
man" we derive, by this operation, the two sentences "every- 
thing is a man" and "something is a man", or, as it may be 
phrased, " *x is a man' is always true" and " ^x is a man' is some- 
times true". The variable "at" here is to be allowed to take all 
values for which the sentence "at is a man" is significant, i.e,, 
in this case, all values that are proper names. 

When we generalize a relation R — say a dyadic relation 
the process is the same, except that, when we substitute a variable 
"S", the possible values of "S'* are confined to dyadic relations 
by the conditions of significance. Take, for example, the advice 
to be all things to all men. If I succeed in obeying this precept, 
that means that, if x is any man and R any dyadic relation, I have 
the relation R to x; in other words, every sentence of the form 

AT is a man, I have the relation R to a:" is true. Or take the 

statement "no two men are wholly unrelated". This means that, 
i£x and j^ are men, some sentence of the form "a: has the relation 

R to y" is true. That is to say, every sentence of the form "if x 
and y are men, some sentence of the form *jc has the relation R 

9 •_ ^. 99 

to y IS true is true. 





It should be observed diat the relations that occur in the above 
development, whether they are constants or variables, are relations 
in intension, not in extension. 

Sentences involving generalization of predicates occur fre- 

stitute an ''adequate" language, i.e., one into which 

quently in common speech. Examples are "Napoleon had all the 
qualities of a great general" and "Elizabeth had the virtues of 
both her father and her grandfather, but the vices of neither". 

do not commit myself to the historical accuracy of this 

For reasons which will appear in Chapter XIX, I shall call the 
assemblage of sentences obtained from atomic judgments of per- 
ception by the three operations of substitution, combination, and 

generalization, the atomistic hierarchy of sentences. 

is an important question whether this hierarchy can con- 
any state- 
ment in any language can be translated. This question has two 
parts : first, can we be content with atomic sentences as the basis 
of the structure ? second, can we be content with names, predi- 
cates, dyadic relations, etc., as our only variables, or do we need 
variables of other kinds ? The first of these questions will be dis- 
cussed in Chapters XIX and XXIV. The second, which is con- 
cerned with generalization and is relevant in solving the paradoxes, 
must be discussed now. 

Generalization raises much more difficult problems than are 
raised by substitution or combination. The main question to be 
discussed in this chapter is : does generalization as above defined 
suffice for mathematical logic ? or do we need variables of kinds 
not definable by means of the above kinds .'^ 

First let us observe that 


if "every sentence of the form f(x) 

is true" or "some such sentence is true" is to have any definite 
significance, the range of values of which ":%;" is to be capable 
must be definite. If we have any extrinsic range of values, such as 

have to be stated. Thus "all 
men are mortal" cannot be interpreted as "all sentences of the 
form 'x is mortaP are true, where the possible values of x are 
men", for this is not derived merely from the function "jf is 

men or 

natural numbers^ this will 



mortal".* The only way in which "all sentences of the form 
yipcf are true" can be derived merely from the function is to 
allow X to take all values for which "/(x)" is significant* So long 
as we confine ourselves to names and relations as variables, 
the principle of substitution secures what is wanted in this 

We need, however, at the very beginning of mathematical 
logic, another sort of variable, namely variable propositions. We 
want to be able to enunciate the law of contradiction and the law 
of excluded middle, i.e. "no proposition is both true and false" 
and "every proposition is either true or false". That is to say, 
"every sentence of the form *it is false that p is both true and 
false* is true", and "every sentence of the form /? is either true 

or false' is true". Here the conditions of significance require that 

should be a sentence (or proposition), but do not^ prima facky 

<( 99 


place any other restriction on "/?". The trouble is that we have 
apparently framed sentences which refer to all sentences, and 
therefore also to themselves. 

More generally, if /(p) is a propositional function of a pro- 
positional variable /?, then "every proposition of the form f{p) 
is true", if admissible, is also a proposition. Is it a possible value 
oi p in *y(/3)" ? If it is, there is included in the totality of values 
oip a value defined in terms of that totality. This has the conse- 
quence that whatever collection of propositions we assign as the 
totality of values of je?, we must be wrong, since there is another 
value of p defined in terms of that totality, and changing as the 
totality changes. The situation is analogous to that of Jourdain's 
Chinese Emperor and the nests of boxes* This Emperor attempted 
to enclose all nests of boxes in one room. At last he thought he 
had succeeded, but his Prime Minister pointed out that the room 
constituted another nest of boxes. Though the Emperor cut oif 
the Prime Mirxister's head, he never smiled again. 

Variable propositions thus involve difficulties, which come 

* In Chapter XVIII we shall develop a theory of general beliefs which tiiight 
seem inconsistent with what is said above. But the inconsistency is only apparent, 
since here, but not there, our problem is purely syntactic. 



to a head in the contradiction of the liar,* I suggest that variable 
propositions are only legitimate when they are an abbreviation 
for name-variables and relation variables. Let *y* be a variable 
which can stand for any sentence constructed by means of our 
three principles of substitution, combination, and generalization. 
Then we may say that "every sentence of the form/(p) is true" 
is not a single new sentence, but a conjunction of an infinite 
number of sentences, in which the variables are not sentences. 

For this purpose, we proceed as follows. We first interpret 
the statement that, if **p" is an atomic sentence, then "/(/?)" is 
true. This is obviously equivalent to: whatever possible values 

1 and Xi may have,/{Ri(xi)} is true; whatever possible values 
Rg and Xi and x^ may have, /{RgC^i, ^2)} is true; and so on. 
Here the variables are only x's and R's. 

We now proceed to the case in which "y is a molecular sen- 
tence. We shall assert that, for all possible values of the x*s 
andy s and of R and S 

/{R(^i5 ^2 • • • ^m) I S(yi,y2 • • • yn)} 


is true; and we shall proceed to similar assertions when the 
argument to/contains not only one stroke, but any finite number. 
Thus we shall now have interpreted the assertion that "/(/>) 
is true when "/?'* is any molecular proposition. 

Finally, we allow "/?** to be any sentence obtained from any 

one of our previous values of "/>" by generalization. 

We thus obtain an interpretation of " */"(/?) * is always true 
if/? is a sentence in the atomistic hierarchy'*. The interpretation 



however, makes this into many sentences, not one. If **f(j>) 
is such that, when "/?" belongs to the atomistic hierarchy, so 
does "/(/>)", then all these many sentences belong to the atomistic 
hierarchy, and no sentence of a new sort has been generated. 

We shall treat "some sentence of the form */(/?)' is true" in 
an exactly similar way, treating it as an infinite disjtmcdon consist- 
ing of the same terms as those in the above infinite conjunction. 

Of course, technically, we can still use the variable "/?". The 


See the opening of Chapter IV, 



only use of the above analysis, technically, is to prevent us from 
regarding "/(/?) is always true" as a possible value of "j?" in 

*'/(/')"• That is to say, "/(/?) is always true ' does not permit us 

to infer "/{/(/?) is always true}". This is important, since 


assertions referring to the totality of possible values of "/?" (or 
of any other variable) are to have any definite significance, they 
must not themselves be among the values that "jt?" can take. 

We have next to consider variable functions. Let us denote 
by "^cz" a variable proposition, in the atomistic hierarchy, in 

which the name "c" occurs, and let "/(/?)" be some definite 
function of propositions belonging to the fundamental hierarchy. 
"We can then form the function 

in which die variable is ^, and we can consider "/(^cz) is true 
for every ^" and "/(<^a) is true for some <^". 

Quite common sentences may be of this form; e.g. "Napoleon 
III had all the vices of his uncle and none of his, virtues", or what 
the drunken man said to the expostulating parson: "there must 
be some of all sorts, and I am of that sort". 

Exactly the same sort of difficulty arises here as in relation to 

"/(/?) is true for every/?". It would seem that"/(^a) is true for 




every ^" is itself a function of a, and that therefore *y( 
true for every ^" ought to imply "/{/(^a) is true for every ^^\ 

But in that case there are values of ^ defined in terms of the 
totality of values of ^, and every conceivable definition of the 
totality of values of (f> can be shown to be inadequate. 

Let us attempt to clarify the matter by some illustrations. 



do not 

What, for example, is meant by "Napoleon III had all the vices 
of Napoleon I".^ First, what is a "vice".? Perhaps we may define 
it as "a habit of which every instance is a sin 
want so serious an analysis, since my purpose is merely to illus- 
trate a point in syntax. For my purpose, we may treat a "vice" 
as a predicate of a certain kind. Thus if "Ri" stands for a variable 

predicate, "R^ is a vice" is of the form "F(Ri)". Now let us put 


for "Napoleon III 




for "Napoleon 







'Napoleon III had all the vices of Napoleon I" becomes: 


'every sentence of the form: *F(Ri) and Ri(i) together imply 
^(a)' is true", where "Ri" is the variable. This, however, is not 




IS to 

yet quite satisfactory, because "F(Ri)", prima facie^ treats 

as if it were a proper name and not a predicate. If "F(Ri)' 
be of a form admitted by the restriction to the atomistic hierarchy 
this must be remedied. We may take "vicious" as a predicate appli- 
cable to individuals, and a "vice" as a predicate implying vicious- 


ness. Thus if "V(jc)" means "at is vicious", "R 


1 is a vice means : 

"sentences of the form *Ri(j^) implies V(a:) for all possible values 
o(x' are true for all possible values of Rj". This must now replace 




in the above analysis of our example. The result may 

seem somewhat complicated, but even so it is still made arti- 
ficially simple for purposes of illustration. 

Let us take another illustration, which will, incidentally, show 
the necessity of distinguishing between properties which involve 
a variable predicate and those that do not. Let our illustration be 
"Pitt was a typical Englishman". We may define a member of a 

"typical" if it possesses all predicates possessed by a 



majority of the class. Thus we are saying that Pitt had every 

predicate R^ which is such that the number of x's for which 

Ri(jc) and x is English" is true exceeds the number for which 
not-Ri (:!!:) and x is English" is true. This is all very well, but if 


instead of "predicate" we had used the general word "property", 
we should have found that there could be no typical Englishman, 
because most Englishmen possess some property which most 
Englishmen do not possess, e.g., that of being between 5 ft. 10 in. 
and 5 ft. 11 in. in height or some analogous determination. 
That is to say, it is untypical to be typical. This shows that 
we run risks if we attempt to speak about "all possible statements 

We shall avoid the trouble if the variable ^, like the variable/? 
is merely a convenient abbreviation for other variables 
positions in which a occurs will be 




(I) Ri(a), IL(a, 


R,(a, i, 

c), etc. 






(2) Combinations of the above with one or more propositions 
in the atomistic hierarchy. 

(3) Generalizations of propositions in (2), provided a is not 
replaced by a variable. 

Thus "/(^fl) is true for every ^" will assert that 


', ' 


( ^ 

(a) Ri(a), Ri(<z,3), etc., are true for all possible values of 




■1 ' 

I \ 

1 I 

I r 

5 etc 

(h) Similar statements as regards Ri((2) | Ri(^), etc. 
(c) Generalizations of (^), which will be found to be merely a 

repetition of (J>). 

In this way the variable 0, like the variable/?, can be reduced to 
name-variables and relation-variables, at the cost of making 



is true for every ^" an infinite number of sentences 

instead of one 


In a language of the second order, **/(/?) is true for every />" 
) is true for every ^'*, can be admitted as single sentences 

This is familiar, and I need not dwell upon it. In the language of 
the second order, variables denote symbols, not what is sym- 

There is therefore no reason to admit as fundamental any 
variables except name-variables and relation-variables (in inten- 
sion). Given the assemblage of propositions that are neither 
molecular nor general, we can — ^so I conclude — construct, from 
this assemblage, an adequate language, so far as mathematical 
logic is concerned, employing only the principles of combination 
and generalization. 

The question of the principle of atomicity remains. This is a 
question concerning the propositions that are neither molecular 
nor general. It is the question whether all of these are of one or 
other of the forms 

Ri W, R2(a, b\ R^Ca, b, c) 


Such propositions as "I believe Socrates was Greek" are, prima 
^Tcie^ not of any of these forms. Still more difficult is "I believe 









that all men are mortal", where the generality is applicable only to 
a subordinate proposition. My belief is not equivalent to: ''i( x 

is a in^^^5 ^ believe that x is mortal", for I may have never heard 

of jc and then I cannot believe him to be mortal. Propositions of 
the form **A is part of B" also raise difficulties. I shall discuss the 
principle ^f atomicity in later chapters. 

remains one question concerning generalization, and 
that is the relation of the range of the variable to our knowledge. 
Suppose we consider some proposition ^'f(x) is true for every x'\ 
e.g, **for all possible values of jc, if x is human, x is mortal". 
We say that if "a" is a name, "/(^) is true for every x" implies 

"y(a)'** We cannot actually make the inference to "/(a)" unless 
**a'* is a name in our actual vocabulary. But we do not intend 
this limitation. We want to say that everything has the property 
fl not only the things that we have named. There is thus a hypo- 
thetical element in any general proposition; "/(at) is true of 

r" does not merely assert the conjunction 

ajbyC . . . are the names (necessarily finite in number) 
that constitute our actual vocabulary. We mean to include 

will be named, and even whatever could be named. 
This shows that an extensional account of general propositions 
is impossible except for a Being that has a name for everything; 
y and even He would need the general proposition: "everything 

is mentioned in the following list: a, iyC, . . J\ which is not a 

purely extensional proposition. 








Chapter XIV 


Language serves three purposes : (i) to indicate facts, (2) to express 
the state of the speaker, (3) to alter the state of the hearer* These 
three purposes are not always all present. If, when alone, I prick 
my finger and say "ouch", only (2) is present. Imperative, in- 
terrogative, and optative sentences involve (2) and (3), but not 
(i). Lies involve (3), and, in a sense, (i), but not (2). Exclamatory 
statements made in solitude, or without regard to a hearer, involve 
(i) and (2), but not (3). Single words may involve all three, for 
instance if I find a corpse in the street and shout "murder !" 

Language may fail in (i) and (3): the corpse may have died 
a natural death, or my hearers may be sceptical. In what sense 
can language fail as regards (2) } Lies, mentioned above, do not 
fail in this respect, since it is not their purpose to express the 
state of the speaker. But lies belong to the reflective use of lan- 
guage; when language is spontaneous it cannot lie, and cannot 
fail to express the state of the speaker. It may fail to communicate 

what it expresses, owing to differences between speaker and hearer 

m the use of language, but from the speaker's point of view 
spontaneous speech must express his state. 

I call language "spontaneous" when there is no verbal inter- 
mediary between the external stimulus and the word or words 

at least this is a first approximation to what I mean by "spon- 
taneous". It is not an adequate definition, for two reasons: first, 
that the intermediary to be excluded need not be verbal, though 
it must have something in common with what is verbal; second, 
that the stimulus need not be, in any ordinary sense, "external". 
The second point being the simpler, let us consider it first. 

Suppose I say "I am hot", and suppose that I say so because 





I am hot. The stimulus here is a sensation. Suppose I say "there 
is a red flower'*, because (in ordinary parlance) I see a red flower. 


The immediate stimulus is again a sensation, though 

the sensation to have outside causes, and, if it has not, my state 

ment is false. When I say "I am hot", I may not expect others 


be hot, for instance if I have been running on a frosty day. 

But when I say "there is a red flower" I expect others to see it 
too. If they do not, I am surprised, which shows that what 
think they will see was part of what I was asserting. The state- 
ment "I see a red patch of a certain shape" is therefore logically 
simpler than "I see a red flower". But "I see a red patch" is on 
a level with "I am hot". It is, however, less spontaneous than 
**I see a red flower" or "there is a red flower". 

Thus instead of saying that a stimulus is "external" we shall 
say that, in "spontaneous" speech, the stimulus is a sensation. 

We must now consider what sort of intermediaries between 
stimulus and words are to be excluded in defining "spontaneous'* 
speech. Take the case of a ready lie. The schoolboy, asked 

angrily "who made the world.'*" replied without a moment's 

hesitation "please, sir, it wasn't me". Ethically, though not 

theologically, this was a lie. In such a case, the stimulus to the 
■words is not what the words mean, nor even something having 
a close causal connection with what the words mean; the stimulus 


is solely the desire to produce a certain effect upon the hearer. 
This requires a more advanced knowledge of language than is 
involved in its merely exclamatory use. I think that, in defining 
^'spontaneous" speech, we must give a subordinate place to the 
desire to affect the hearer. In certain situations, certain words 
occur to us, even if we do not utter them. The use of words 

' wheti the situation causing it can be defined 



without reference to the hearer. Spontaneous speecli is such as 

might occur in solitude. 

Let us confine ourselves for the present to speech that is spon- 
taneous and indicative. I want to cqnsider, in relation to such 
speech, the relation between (i) indicating facts, and (2) expressing 
the state of the speaker. 


' ^ 







- I 






t ' L 












t' ^ 

'1 >. ft 



K 'y);i\ 



r ' 



I K 

1 1 1' 

L ■■ 



* % 


I 4f 


I I 




h 4 


I I 

■ ^j . 

1 1* 

4 ^ J 11 X ri 





1 , '> '^ 

,1* "','i 

t I 

*M ■'■?', 

1» H 


n 1 ■ 

^ V u 



^ . -*. 



In some cases, the distinction between (i) and (2) seems to be 

non-existent. If I exclaim 






the fact indicated is a 

state of myself, and is the very state that I express* The word 


hot" means a certain kind of organic condition, and this kind 

of condition can cause the exclamatory use of the word 



In such cases, the cause of the instance of the word is also an 
instance of the meaning of the word. This is still the case with 


see a red patch 







Where, as in 

from certain reservations as to the 

cases, there is no distinction 

between (i) and (2), the problem of truth or falsehood does not 
arise, for this problem is essentially connected with the distinction 
between (i) and (2), 

Suppose I say "you are hot", and suppose I believe what I 
say. In that 

case, I am 


' my state and "indicating* 
yours- Here truth and falsehood come in, since you may be cold 
or you may even not exist. The sentence "you are 



one sense 


IS, m 
significant" if it can express a state of me; in what 
is perhaps another sense, it is "significant" if it is true or false. 
Whether these are or are not different senses of "significant" 
cannot be decided until we have defined "true" and "false". For 
the moment, I shall confine myself to the first definition : I shall 

consider a sentence "significant" primarily if it actually expresses 
a state of myself, and from this starting-point I shall endeavour 
gradually to reach a wider definition. 

What is happening in me when my state is expressed by the 
words "you are hot"? To this question there is no definite 
answer. I may be "imagining" a sensation of heat combined with 
the sensation of touching you. I may be expecting you to say 

I am hot". I may see beads of sweat on your face, and 


an inference. All that can be said definitely is that certain possible 
occurrences would surprise me, while certain others would give 
me a feeling of confirmation. 

believe you are hot" expresses a different 

"you are hot": the fact that it 

The statement 


state from that expressed 

indicates is the fact expressed by "you are hot". The question 

arises: can the statement "I believe you are hot" be replaced 



by an equivalent statement referring only to myself, and not 

mentioning you ? 

Such a statement, I incline to think, would be possible, but 
very lengthy and complicated. It is customary to describe "states 
of mind^* by words having an external reference :. we say we are 
thinking ^this or that, wishing ^or this or that, and so on. 
We have no vocabulary for describing what actually takes place 
in us when we think or desire, except the somewhat elementary 
device of putting words in inverted commas. It may be said that 
when I think of a cat, I thitik "cat"; but this is both inadequate 
and not necessarily true. To think "of" a cat is to be in a state 
in some ^vay related to the percept of a cat, but the possible 
relations are numerous. The same applies in a stronger degree 
to belief. We have thus a twofold difficulty: on the one hand 


that the occurrences which can be correctly described as believing 
a given proposition are very various, and on the other hand that 
we need a new vocabulary if we are to describe these occurrences 
otherwise than by reference to objects. 

What must be occurring when I am believing the proposition 


*Mr. A is hot"? Mr. A need not be occurring: he may be a 

purely imaginary person, whom in a dream I see in hell. No 

words need be occurring. I have seen water steaming when it 
was at freezing point ; I might (if I had had less knowledge) have 
plunged my hands into it in the belief that it was hot, and have 
received a shock of surprise from the perception of its coldness, 
and in this case the belief could have been quite wordless. On 
the other hand, there must be in me something corresponding to 
the word "hot", and something which, perhaps mistakenly, is 
Je/t as a sign of a person called "Mr. A'*. It is almost impossible 
to make such statements sufficiently vague, but I am doing my 


The one word "belief" should, I think, be replaced by several. 
First: perception, memory, expectation. Next come habit-in- 
ferences, of the kind that Hume considers in connection with 
causation. Last come deliberate inferences such as logicians 
sanction or condemn. It is necessary to distinguish these in our 



present discussion, because they produce difFerent states of the 
believer. Suppose I am a Dictator, and at 5 p.m. on October 22nd 
some one attempts to stab me with a dagger. As a result of reports 
by the secret police, I believe that this is going to happen; this 
is (or at least may be) a logically inferential belief; it may also 
be a belief produced by habit-inference. At 4.59 I see a known 
enemy taking a dagger from its sheath ; at this moment I expect 
the assault. The inference to the immediate future now -is not 
logical, but habitual. A moment later, the assassin rushes forward, 
the blade pierces my coat, but is stopped by the shirt of chain 

armour that I wear next the skin. At this instant, . my belief is 
a matter of perception. Subsequently, the villain having been 
beheaded, I have the experience of "emotion recollected in tran- 
quillity", and my belief has become one of memory. It is obvious 
that my bodily and mental state is difFerent on these four occa- 

sions, though what I am believing is the same throughout, in 
the sense that it can be indicated in the same words, viz. "I 
believe that at 5 p.m. on October 22nd an attempt is made to stab 
me with a dagger". (The "is" here is timeless, not the present 
tense; it is like the "is" in "4 is twice 2", 

It is perhaps convenient to exclude perception from the forms 
of belief. I have included it above* for the sake of the serial 

development. But in general I have excluded it. 

Our problem may be stated as follows. There are a number 
of states of my mind and body, any one of which, when it exists, 

makes it true to say "I believe you are hot". We may assume 

that any one of these states can be described with sufficient 

accuracy by psychologists and physiologists. Assuming this has 

been done for all such states, will the psycho-physicist be able 

to know, concerning any one of them, that it is a case of believing 

you to be hot } And further, will he b^ able to discover anything 

in common among the states except their relation to you and 
hotness } 

I think that in theory the. answer to both questions should be 
in the affirmative. Essentially the problem is the same as that of 
discovering that "hot" means hot, which most children solve 



in about 1 8 months. If I am in any state that can be described 
as believing that you are hot, and you say "do you believe I am 
hot?" I shall answer that I do. This is an experimental causal 
property of the belief, quite as satisfactory as those that are used 
in chemical tests. There are of course complications— mendacity 
difference of language 
difficulty of principle. 

We can now say: the states of two persons who speak the 
same language are instances of the same belief if there is a sen- 
tence S such that each, in reply to the question: "do you believe 




but none of these afford any 





I do 

9> 9(( 

The person who, to himself or to any one 

to deceive, says 


S\"y believes S. Two 

will reply '"'certainly, I have just said so" 

that he does not wish 
sentences S and 5*' have the same significance if whoever believes 
the one believes the other. Experimentally, in this case, if you 
hear a man %ay "5" and you ask him "do you believe S' ?'\ he 

This applies if, for 
example, "5" is "Brutus killed Caesar" and "»S'" is "Caesar was 
killed by Brutus". The same applies if S and S' are in different 
languages, provided both are known to the persons concerned. 
One purpose of this discussion is to decide whether "A believes 
" is a function of p. Let us substitute for thei proposition p 
a sentence j. In logic, we are accustomed to thinking of either 
a proposition or a sentence primarily as capable of truth or 

we can, I think, at least for the time being, discard 


propositions and concentrate on sentences. The essential point 

technically, is that we are concerned with the arguments to truth* 


functions. If "^" 


"r" are two sentences, "j or r" is a third 
sentence, whose truth or falsehood depends only upon the truth 
or falsehood of s and r. In logic, sentences (or propositions) 
are treated technically as if they were "diings". But a sentential 
utterance, in itself, is merely a series of noises, of no more interest 
than a series of sneezes and coughs. What makes a sentence 

* I do not suggest that this is the best definition of what constitutes the "same" 
belief. The best definition would be one taking account of the causes and effects 
of the belief. But this definition would be elaborate and difficult, and the above 
definitioa by means of sentences seems to suffice for our present purposes. 



interesting is its significance, or, to be more specific, its capacity 
for expressing a belief and for indicating a fact (or failing to do 

so). It acquires the latter through the former, and the former 
through the meanings of its words, which meanings are causal 
properties of noises acquired through the mechanism of con- 
ditioned reflexes. 

From what has just been said it follows that the relation of 
a sentence to the fact that makes it true or false is indirect, and 
passes through the belief expressed by the sentence. It is primarily 

the belief that is true or false. (I am for the present abstaining 
from any attempt to define "true" and "false".) When, therefore, 
we say that "^ or f" is a sentence, we must give substance to our 
statement by investigating the belief expressed by "j or r" 




seems to me that a person or animal may have a belief correctly 
expressed by "^ or t*\ but describable by the psycho-physiologist 
without the use of the word "or". Let us investigate this matter 
remembering that what is said about "or" is likely to apply to 
other logical words. 

I suggest that there is a difference between the word "or" and 
such words as "hot" or "cat". The latter words are needed in 
order to indicate as well as in order to express, whereas the word 
or" is needed only in order to express. It is needed to express 
hesitation. Hesitation may be observed in animals, but in them 
(one supposes) it does not find verbal expression. Human 
beings, seeking to express it, have invented the word "or 

The logician defines "/? or j" by means of the conception of 
"truth", and is thus able to short-circuit the route through the 
belief expressed by "/? or q\ For our purposes, this short-circuit 
is not available. We wish to know what are the occurrences that 
make the word "or" useful. These occurrences are not to be 
sought in the facts that verify or falsify beliefs, which have no 
disjunctive quality, but are what they are. The only occurrences 
that demand the word "or" are subjective, and are in fact hesi- 
tations. In order to express a hesitation in words, we need "or 
or some equivalent word. 

Hesitation is primarily a conflict of two motor impulses. 




may be observed, for instance, in a bird timidly approaching 
crumbs on a window-sill, or in a man contemplating a dangerous 
leap across a chasm in order to escape from a wild animal. The 
intellectual form of hesitation, which is expressed by a disjunction, 
is a development from purely motor hesitation. Each of the two 
motor impulses, if it existed alone, would be a belief and could 

be expressed in an assertion. So long as both exist, no assertion 
is possible, except a disjunction, "this or that". Suppose, for 
example, that you see an aeroplane. In ordinary circumstances, 
you will be content to note "there is an aeroplane". But if you 
are in charge of an anti-aircraft gun, the action called for will 
be different according to what sort of aeroplane it is. You will 
say, if you are in doubt, "that aeroplane is British or German". 
You will then suspend all action except observation until you 
have decided the alternative. The intellectual life is mainly con- 
cerned with suspended motor impulses. Consider a young person 
cramming for an examination. His activity is governed by a dis- 
junction: "I shall be asked A or B or C or . . ." He proceeds to 
acquire motor habits appropriate to each of these alternatives, 
and to hold them in suspense until the moment when he learns 
which of them to let loose. His situation is thus closely analogous 
to that of the man with the anti-aircraft gun. In either case the 
state of mind and body of the doubter can, theoretically, be 
specified by a description of the motor impulses and their conflict 
without the use of the word "or". The conflicts of course, is 

, V* ^V/MACIV., 

to be described in psycho-physical terms, not in terms of logic. 

Similar considerations apply to the word "not". Imagine a 
mouse which has frequently observed other mice caught in traps 

baited with cheese. It sees such a trap and finds the smell of the 
cheese attractive, but memory of the tragic fate of its friends 
inhibits its motor impulses* It does not itself use words, but we 
can use words to express its state, and the words to use are: 
"that cheese is not to be eaten". At one time I kept pigeons, 

and found them to be models of conjugal virtue. But I once 
introduced among them a new hen pigeon very like one of the 
previous married hens. The husband mistook the new hen for 



his wife, and began cooing round her. Suddenly he discovered 
his mistake, and looked just as embarrassed as a man would look 
in similar circumstances. His state of mind could have been ex- 

pressed in the words: "that is not my wife'". The motor impulses 
associated with the belief that it was his wife were suddenly in- 
hibited. Negation expresses a state of mind in which certain 
impulses exist but are inhibited. 
Speaking generally, language of the sort that logicians would 

has two functions: to indicate a fact, and to 


call "assertion" 


express a state of the speaker. If I exclaim * 
a blaze and express a state of my perceptive apparatus. Both the 
fact indicated and the state expressed are in general non-verbal 
Words are of two sorts: those that are necessary in order to 
indicate facts, and those that are only necessary in order to 

express states of the speaker. Logical words are of the latter sort. 

The question of truth and falsehood has to do with what words 

and sentences indicate, not with what they express. This, at least, 

is what one might hope. But how about lies ? It would seem that, 

when a man lies, the falsehood is in the expression. A lie is still 
a lie if it happens to be objectively true, provided the speaker 
believes it to be false. And how about sheer mistakes.'^ Psycho- 

analysts tell us that our beliefs are not what we think they are, 
and certainly this is sometimes the case. Nevertheless there seems 
to be some sense in which there is less chance of error as regards 
the expression than as regards the indication. 

The solution lies, I think, in the conception of "spontaneous" 
speech, which we considered earlier in this chapter. When speech 

is spontaneous, it must, I think, express the speaker's state of 
mind. This statement, rightly interpreted, is tautological. A given 
belief, we agreed, may be shown by various states of the organism, 
and one of those states is that of spontaneously pronouncing 
certain words. This state, being easier to observe than those that 
involve no overt behaviour, has been taken as the definition of 

a given belief, whereas it is in fact merely a convenient experi- 
mental test. The result has been an unduly verbal theory of 
truth and falsehood and logical words generally. When I say 



"unduly", I mean unduly from the standpoint of theory of know- 
ledge; for logic, the traditional acceptance of "propositions" and 
the definition of (e.g.) disjunction by means of truth-values are 
convenient and technically justified, except in relation to certain 
crucial problems such as extensionality and atomicity. These 
problems, since they arise in connection with prepositional atti- 
tudes (believing, etc.), can only be dealt with by means of theory 
of knowledge. 




Chapter XV 


When "truth" and "falsehood" are regarded as applicable to 
sentences, there are, from the standpoint of theory of knowledge, 
two kinds of sentences: (i) those whose truth or falsehood can 
be inferred from their syntactical relation to other sentences, 
(2) those whose truth or falsehood is only derivable from a rela- 
tion to something that may be called "fact". Molecular and general 
sentences may, for the moment, be regarded as of the first kind 
whether this is strictly true we shall consider at a later stage. 
The problems with which we are concerned in the present work 


arise only in regard to sentences of the second kind, for, if we 

have defined "truth" and "falsehood" for such sentences, the 
problems that remain belong to syntax or logic, which is not 
our subject. 

Let us, then, confine ourselves, to begin with, to indicative 

sentences of atomic form, and ask ourselves whether, in regard 

to such sentences, we can frame a definition of the words "true" 
and "false". 

We agreed in the last chapter that an indicative sentence "ex- 
presses" a state of the spesJcer, and "indicates" a fact or fails 
to do so. The problem of truth and falsehood has to do with 
"indication". It appeared that truth and falsehood apply primarily 

to beliefs, and only derivatively to sentences as "expressing** 

The distinction between what is expressed and what is indi- 
cated does not always exist — for instance, if I say "I am hot", 
what is expressed is always a present state of the speaker ; what 
is indicated may be such a state, but usually is not What is 
expressed and what is indicated can only be identical when what 




is indicated is a present state of the speaker. In this case, if what 

is spoken is "spontaneous" in the sense defined in the last chapter, 
the problem of falsehood does not arise. We can therefore make 
a beginning . by saying : a spontaneous sentence which indicates what 
it expresses is 

^^tru£* by definition. 

But now suppose that, pointing at a visible object, I say "that 
is a dog". A dog is not a state of myself; consequently there is 
a difference between what I indicate and what I express. (The 
phrase "what I indicate" is open to objection, since, in the case 
of falsehood, it may be contended that I fail to indicate anything, 
but I shall employ it to avoid circumlocution.) What I express 
may be inferred from what would surprise me. If the shape that 

see suddenly vanishes, without the possibility of eclipse 
some other .object, I shall be amazed. If you say to me : all the 
doors and windows are shut; there are no hiding-places in the 
room ; and I am sure that a moment ago no dog was here ; I shall 
conclude, if I have been reading Faust^ that what I saw was not 

a dog but Mephistopheles. If the object that I am watching 
suddenly begins, like the pug in Heine's Atta Trolly to talk 
German with a Swabian accent, I shall conclude, as Heine did 
that it is a Swabian poet transformed by a wicked witch. Such 
occurrences, no doubt, are unusual, but they are not logically 



Thus when I say "that is a dog", certain more or less hypo- 
thetical expectations are part of the state that I express. I expect 
that, if I watch, I shall continue to see something like the shape 

that led to my remark ; I expect that, if I ask a bystander who 

has been looking in the same direction, he will say that he also 
saw a dog ; I expect that if the shape begins to make a noise, it 
will bark and not talk German. Each of these expectations, being 
a present state of myself, can be both expressed and indicated 
by a single sentence. Suppose, to be definite, that I actually, not 
hypothetically, expect a bark; I am then in the state called "lis- 
tening' ' 


and I may very possibly have an auditory image of a 

bark, or the word 




though both may be absent. We have 

here the smallest gulf between expression and indication 



if I 






in a moment 

shall hear a bark" 


express my present 

expectation and indicate my future sensation. In this case, there 
is a possibility of error: the future sensation may not occur. 

Known error is, I think, always of this kind; the sole method 
of discovering error is, I believe, the experience of surprise owing 
to a disappointed expectation. 

There is, however, still a difficulty. I have at every moment 
a large number of more or less latent expectations, and any one 
of these, if disappointed, gives way to surprise. In order to know 
which expectation was false, I must be able to relate my surprise 
to the right expectation. While I am expecting the dog to bark, 
I may be surprised to see an elephant walking along the street; 
this surprise does not prove that I was wrong in expecting the 
dog to bark. We say we are surprised at something ; that is to 

say, we experience not merely surprise, but surprise related to 
a present percept. This, however, is still not enough to make 
us know that our previous expectation was erroneous; we must 
be able to relate our present percept to our previous expectation, 
and, moreover, to relate it in a negative way. Expectation makes 

us say "the dog will bark"; perception makes us say 


the dog 

is not barking"; memory makes us say "I expected the dog to 
bark". Or we may expect the dog not to bark, and be surprised 
when he does. But I do not see how this simplest case of known 
error can be dealt with except by the above combination of 
expectation, perception, and memory, in which either the expec 
tation or the perception must be negative. 

The emotion opposite to surprise may be called confirmation; 
this arises when what has been expected happens. 

We may now say, as a definition: an expectation as to an 
experience of my own is true when it leads to confirmation, and 
false when it leads to surprise. The words "leads to", here, are 
an abbreviation for the process just described. 

But when I say "there is a dog", I am not merely making 

an assertion as to my own experiences, past, present, or future; 
I am stating that there is a more or less permanent thing, which 
can be seen by others, exists when unseen, and has a sentient 







life of its own 

am assuming 

that I am a plain man, not a 

solipsistic philosopher.) The question "why should I belie\ 

all this ?" is an interesting one, but is not the one I wish to dis- 
cuss at the moment. What I wish to discuss at the moment is: 
what is there on the side of expression corresponding to this 
indication of something outside my experience? Or, in old- 

fashioned language, how do I think of things that 




I find in almost all philosophers a great unwillingness to face 
diis question. Empiricists fail to realize that much of the 
knowledge they take for granted assumes events that are not 
experienced. Those who are not empiricists tend to main- 
tain that we do not experience separate events, but always 
Reality as a whole; they fail, however, to explain how we 

distinguish between (say) reading poetry and having a tooth 

pulled out. 

Let us take an example. Suppose on a fine Sunday I go out 
for the day with my whole family, leaving my house empty; 

when I return in the evening, I find it burnt down, and am in 

formed by neighbours that the fire was first noticed too late for 
the fire-engines to be able to put it out. Whatever my philosophy, 
I shall believe that the fire began in a small way, as fires do, and 
therefore existed for some time before any human being per- 
ceived it. This, of course, is an inference, but it is one in which 




I feel great confidence. The question I wish to ask at the moment 


is not "is this inference justifiable.'*", but rather: 
inference justifiable, how am I to interpret it.'*" 


If I am determined to avoid anything not experienced, there 

are several things that I can say. I can say, 

like Berkeley, that 

God saw the beginning of the fire. I can say 





unfortunately, is full of ants, and they saw it. Or I can say that 
the fire, until it was seen, was merely a symbolic hypothesis. 
The first of these suggestions is to be rejected because such uses 
of God have become against the rules of the game. The second 
is to be rejected because the ants are accidental, and the fire could 
obviously have burnt just as well without them. There remains, 



then, the third suggestion, which we must try to make more 


We may state this theory as follows : let us first develop 
physics on the usual realistic hypothesis that physical phenomena 
do not depend for their existence upon being observed; let us 
further develop physiology to the point where we can say under 
what physical conditions physical phenomena are observed. Let 
us then say : the equations of physics are to be regarded as only 
connecting observed phenomena; the intermediate steps are to 
be regarded as dealing only with mathematical fictions. The 
process suggested is analogous to a calculation which begins and 
ends with real numbers, but uses complex numbers in the course 

of the argument. 

This theory may be carried further: I may exclude, not only 
events which no one observes, but events which I do not observe. 
We might, to simplify the hypothesis, suppose that observable 
phenomena are those that happen in my brain. We shall then, 
after developing a realistic physics, define the space-time region 
occupied by my brain, and say that, of all the events symbolically 
assumed in our physics, only those whose space-time co-ordinates 
are among those of my brain are to be regarded as "real". This 
will give me a complete solipsistic physics, symbolically indis- 
tinguishable from ordinary realistic physics. 

But what can I mean by the hypothesis that, of all the events 
symbolically occurring in my physics, only a certain sub-class 

I * 



real'*.^ There is only one thing that 

can mean 




: that the mathematical account of a physical event is a 
description, and that such descriptions are to be considered empty 
except in certain cases. The reason for not considering them 
empty in these cases must be that, apart from physics, 
reason to know the events described in these cases. 

Now the only ^vents in which I have reason to believe apart 
from physics (taking physics in a wide sense) are those that I 
perceive or remember. 

It is evident that two hypotheses which have exactly the same 
consequences as regards what I perceive and remember are, for 



me, pragmatically and empirically indistinguishable. The course 
of my life will be exactly the same whichever of them is true, 
and it is analytically impossible that my experience should ever 
give me a ground for preferring one to the other. It follows 
diat, if knowledge is to be defined either pragmatically or in 
terms of experience, the two hypotheses are indistinguishable. 

Convertandoj if it is logically possible to distinguish the two 
hypotheses, there must be something wrong with empiricism. 
The interesting point about this result, to me, is that it only 
requires us to be able to distinguish the two hypotheses, not 
to know which of them is true* 
This brings me back to the question: how can I think of 


things that I cannot experience r 

Take (say) the statement: "sound is due to waves in air*'. 
What meaning can such a statement have ? Does this necessarily 
only mean: "if I suppose sound to be due to waves in air, I shall 

<« J >> 


T^ , 

be able to develop a theory connecting the sounds that I hear 
with other experiences" ? Or is it capable of meaning, as it seems 
to do, that there are events in air that I do not experience ? 

This question turns upon the interpretation of existential pro- 
positions. Logic assumes that, if I understand a statement 
I can understand the statement "there is an x such that <^;t:*'. If 
this is assumed, then, given two understandable statements <j5 
ifta I can understand "there is an x such that ^x and ijsx*'. But 
it may happen that, in my experience, fi>x and ^x are never 
conjoined. In that case, in understanding "there is an x such that 
^x and ^x^\ I am understanding something outside experience; 
and if I have reason to believe this, I have reason to believe that 

there are things which I do not experience. The former is the 

case of unicorns, the latter that of events before my birth or after 

my death. 

The question thus reduces to the following: if "there is an 

X such that <j>x^^ \% not an analytical consequence of one or more 

propositions expressing judgments of perception, is there any 

significance in the statement "I believe that there is an x such 
that <f>x'' } 



Let US take some simple example, such as '*my study exists 
when no one is in k'\ The naive realist interprets this as: "what 

see when in my study exists when I do not see it". To avoid 
the word exist, we can translate this into: "there are events 







my experience which are simultaneous with what I see when in 
my study, but not with my seeing it". This involves a separation 

between seeing and what I see; it also involves the hypothesis 

that what I see is causally independent of my seeing. A very 
little knowledge of the physics of light and the physiology 
vision suffices to disprove the second of these hypotheses, and for 
the first it is hard to find good grounds. The realist is thus driven 
to a Ding-an-sich as the cause of his visual percepts, and to the 
statement that this Ding-an-sick can exist at times when it is not 
causing visual percepts. But we must be able to say something 
about this cause, if our assertion is not to be quite empty. The 
question is: what is the minimum that will save our assertion 
from emptiness ? 

Suppose we say: the sensation of red has one sort of cause, 
and that of green has another. We are then, when we try to 
pass from sensation to physics, attributing hypothetical predi- 
cates to hypothetical subjects. Our inference from sensation 
depends upon a principle of the following form; "there is a 
property ^ such that, whenever I see red, there is something 
having the property ff>\ But this is not nearly enough. To try 
to get more precision, let us proceed as follows. Let "the property 
^ has the property/ *mean* ^ is a shade of colour". 

Then I say there is a correlator S between the members of/ 
and the members of a certain other function F, such that, if 


, »,«W* W*.*U, **, 

in my visual field, ^ has the property /and a has the property ^, 
and if ^ is the argument to F which is correlated to ^, then there 
is an X such that ^ has the property F and x has the property iff. 
It is to be understood that here F and S are apparent variables. 

Let us state this matter somewhat differently. Let us define 
a shade of colour as all the visual places having colour-similarity 
to a given visual place and to each other. Thus a shade of colour 
is a class, and colours are a class of classes, k say. We now assume 



that there is a correlator S between a kind of physical occurrence 

(light- waves of suitable frequency) and a colour. I see a patch 
of which the colour is a, and I take this as evidence of the exis- 
tence of the class which S correlates with a, which I denote 

by '*S°a". That is, I assume that whenever a member of a exists 


a member of S^a exists at roughly the same time. Formally 
this assumption is : 


"If K is the class of shades of colour (each shade being defined 
as all the patches that are of this shade), then there is a one-one 

relation S, whose converse domain is /c, and which is such that, 
a is a /c and a is an a, there is an x which is roughly simul- 
taneous with a and is a member of the class that S correlates 

with a." (i) 

Or, to state the same assumption in other words: 

* 'There is a one-one relation S which correlates classes of 
physical events with shades of colour, and which is such that, 

a is a shade of colour, whenever a patch whose colour is a 
exists, a physical event of the class correlated with a exists at 
roughly the same time.'* (2) 

The above hypothesis is only a part of what we must assume 
we are to believe that cats and dogs exist when we are not 
seeing them. Credible or not, the hypothesis is at least intelligible, 
since it involves only variables and empirically known terms. 
It gives an answer — not the answer — to the question from which 
this discussion started, namely: **how do I think of things that 


cannot experience 

It will be remembered that we phrased this question, at first, 

somewhat differently, namely: "what is there on the side of 

expression corresponding to the indication of something outside 

my experience ?" We seem, however, to have answered a question 

somewhat different from this. It now appears that, if the state- 
ment "there is a dog" is interpreted in the way of naive realism, it 
is false, while if it is interpreted in a way that may be true the 



dog has been transformed into an apparent variable and is no 
longer any part of what is expressed by what I say. 

Let us revert to (i) on p. 221. Here we may say that ;c is **indi. 
cated" by a; a is a patch of colour that we see when we "see a 

dog*', while x may belong to the dog himself. Thus, put too 

schematically, we may say that when I say "I see a dog 

express a and indicate x. But in what I believe, correctly stated 

AT is a mere variable, and is not expressed at all. The case is 
analogous to that in which we wish to use proper names but are 
compelled to use descriptions. 

We may say, generally : when I am in a state of believing, 
that aspect of the believing which seems to refer to something 
else does not really do so, but operates by means of apparent 
variables. To take the simplest case : if I am expecting an explosion, 
the verbal expression of my belief is **there will be a noise". Here 

«<_ ?_^>s 

a noise is an apparent variable. Similarly if I am recollecting 
an occurrence by means of a memory-image, the verbal expression 
of my memory-belief is ''there was something like this", where 
"this" is the memory-image and "something" is an apparent 

We thus arrive at the following results ; when the verbal ex- 
pression of my belief involves no apparent variable, what is 
expressed and what is indicated are identical When the verbal 
expression of my belief involves an existence-statement, say 
"there is an x such that <t>x*\ this, as it stands, is the expression 
of the belief, but the indication is the verijfier of the proposition 

in virtue of which "there is an x such that <^jc" is true, 

or rather it is what would verify "^a" if we could assert 

We cannot assert it, because a lies outside our experience, and 

« J »> 

<< I »> 

<i » 

a is not one of the names in our vocabulary. All this involves 
the assumption that propositions of the form "there is an x such 

that <f>x'' can be known when no proposition of the form 

«< J .99 

IS known— e.g. "that dog stole the leg of mutton when I wasn't 

To sum up: a sentence in the indicative "expresses" a belief; 
it is merely one of an indefinite multitude of acts that can express 


"rxt^r^ 99 


a given belief. If the sentence contains no apparent variable it 
must mention only things now present to the believer ; in that 
case, it is capable of having a peculiar causal relation to these 
things which makes it what, in an earlier chapter, we called a 
"sentence describing an experience"^ If it has this peculiar rela- 
tion, the sentence (and the belief which it expresses) is called 
"true"; if not, "false". In this case, what the sentence "expresses" 
and what it "indicates" are identical, unless, being false, it 
"indicates" nothing. 

But when a sentence goes beyond present experience, it must 
involve at least one apparent variable. If, for the moment, we 
adhere as closely as logic will permit to the metaphysic of common 
sense, we shall say that, when I experience a percept a, there is 
a one-one relation S between some "thing" and a, the "thing" 
being what I should commonly be said to be perceiving. E.g. let 

be a canoid patch of colour ; then S% is the dog that I say I 

am seeing when I experience a. When I say ."this dog is lo 

years old", I am making a statement about S% which involves 
apparent variables* If my statement is true, there is a c such that 
c = S^a; in this case, what I indicate is "c is lo years old", or 

rather, is what makes this true* 

But this is, as yet, very unsatisfactory. In the first place, the 
sentence '*c is lo years old" can never be pronounced, because 
the proper name c does not occur in my vocabulary. In the 
second place, for the same reason, I can never have a belief 
expressible in this sentence. In the third place, we decided that 
sentences are nothing but expressions of beliefs. In the fourth 
place, I made, above, the hypothesis that the sentence "this dog 
is 10 years old" was "true", and so far we have not defined the 
truth" of sentences which contain apparent variables, as this 
sentence does. 

We cannot extricate ourselves from this tangle except by con- 


sidering what is to be meant by the "verifier" of a belief 

belief, when it is sufficiently simple, has one or other of various 
possible causal relations to a certain other occurrence; this 
occurrence is called the "verifier" of the belief, or of any sentence 





expressing the belief. Certain causal relations, by definition, make 
the belief "true"; certain others, "false". But when a belief, 
means of apparent variables, refers to matters outside my expe 
rience, there are certain complications. Let us revert to the illus- 
tration "you are hot", which avoids irrelevant difficulties. This 
may be taken to mean "there is a hotness related to my percept 
of your body as, when I am hot, the hotness of me is related 
to my percept of my body".* When I am hot I can give a proper 
name to my hotness; when you are hot, your hotness, to me, 
is an hypothetical value of an apparent variable. There are here 

two stages. Suppose I represent my percept of my body by 

my percept of your body by 3, my hotness by A, the relation 

which I perceive between, a and A by H, then "you are hot" is 

"there is an A', such that b H A'". 

There is here an hypothetical sentence "i H A'", which I cannot 
utter, because I have no name "A'" in my language. But there 
is also, if you are hot, an actual occurrence, which is hypotheti- 
cally named by the hypothetical name &\ and this occurrence 
is actually so related to b, that its relation to B would be a verifier 
of the sentence "^ H A'" if I could pronounce this sentence. This 
whole state of affairs constitutes the verifier of the sentence "there 
is an k' such that ^HA'". How we come to know all this, if 
we know it, I am not inquiring; I am assuming that I can know 
that you are hot, and asking what is the simplest possible account 
of such knowledge, supposing it to exist. 

We say now that, in the simpler class of cases, what is indicated 
by a sentence is its verifier, when, the sentence is true, but is 
nothing when the sentence is false. 

In the case of "you are hot", I could, if my vocabulary were 
sufficient, frame a sentence containing no variable, which would 
be verified by the same occurrence that verifies my actual sen- 



tence; it is a merely empirical fact that I have not sufficient 
proper names for this purpose. In the case of "all men are mortal" 
the matter is different; no conceivable vocabulary could express 

♦ This is a simplification, but one which does no harm in relation to our 
present problem. I shall attempt a more accurate theory in the next chapter. 




this without variables. The difference is that one occurrence is 
a complete verifier of "you are hot", whereas many occurrences 
are necessary to verify a general statement. From any standpoint 
except that of theory of knowledge, "you are hot" may be inter- 
preted as "^ H A"*; it is only theory of knowledge that requires 
the interpretation "there is an K such that h H A'". 

It will be seen that the relation of a belief or a sentence to what 
it indicates, i.e. to its verifier (if any), is often somewhat remote 

* a verifier means to 

perceive it, we must, unless our knowledge is to be unbelievably 

and causal. Also that, although to "know 

depleted, know the truth of many sentences whose verifiers cannot 
be perceived. Such sentences, however, always contain a variable 

where the name of the verifier would occur if our perceptive 
faculties were sufficiently extensive. 



Chapter XVI 


Preliminary Discussion 

From what has been said so far, it would seem that, if our know- 
ledge is to be roughly coextensive with what we all think we 
know, it must be derived from three sources : 

(i) Beliefs (or sentences) having a certain kind of relation to 
some occurrence, which in general is non-linguistic. 

(2) Principles of logical inference. 

(3) Principles of extra-logical inference. 

Of these three sources, we have so far been concerned only 
with the first. The second we may omit from our consideration, 
since it does not raise the problems as to empirical knowledge 
which we are attempting to solve. The third raises questions of 
very great difficulty, but it cannot be profitably discussed until 
the first is disposed of* 

We may put the matter as follows : given any empirical sen- 
tence which we believe, our reason for believing it may be one 
or more other sentences which we already believe, or may be 
solely some non-linguistic occurrence having a certain relation 
to the sentence believed. In the latter case, the sentence is a "basic 

factual sentence'*. In the former case, in which the sentence is 
inferred, there must be among the premisses of the inference at 
least one basic factual sentence ; the other premisses will belong 
to classes (2) and (3) above* 

In the present chapter, I wish to discuss, not knowledge, but 
truth. What I know must be true, but truth is wider than know- 

ledge in two respects. First, there are true sentences (if we accept 
the law of excluded middle) as to which we have no opinion 
whatever ; second, there are true sentences which we believe and 




yet do not know, because we have arrived at them from faulty 
reasoning, I once met a Christadelphian who held, on grounds 
derived from the Book of Revelation, that there would shortly 
be trouble in Egypt. There was. His belief was true, but not 

"True'* and "false'*, we decided, are predicates, primarily, of 
beliefs, and derivatively of sentences. I suggest that "true" is 
a wider concept than "verifiable'*, and, in fact, cannot be defined 
in terms of verifiability. 

When an empirical belief is true, it is true in virtue of a certain 


occurrence which I call its "verifier". I believe that Caesar was 
assassinated; the verifier of this belief is the actual event which 
happened in the Senate House long ago. My purpose in this 
chapter is to consider the relation of beliefs to their verifiers in 
various kinds of cases. 

Let us begin by reconsidering the case in which A says that B 
is hot. There is, if this is true, an occurrence experienced by B but 
not by A, in virtue of which what A says is true. We interpreted 
this assertion by A as meaning: "there is a hotness related to 
my percept of B's body as my hotness, when I am hot, is related 
to my percept of my body ".This interpretation, however, ignored 
the theory developed in the chapter on proper names, according 
to which "hotness" (or at any rate a specific degree of hotness) 
is a proper name, not a universal of which there is one instance 
in A and another in B. We shall say, if we adhere to this theory, 
that "A is hot" (pronounced by A) asserts a relation between a 
(which is A's percept of his own body) and A, which is hotness. 
The relation involved may be called "compresence". Then "A 
is hot'* (pronounced by A) means "a and h are compresent". 

Now if b is A's percept of B's body, b and h are compresent 
if A is hot^ but not if B is hot while A is cold. 

Therefore in order to interpret "B is hot" (pronounced by A), 
A must somehow describe B's body, or B's percept of B's body. 

as opposed to A's percept of B's body. How is A to describe 
B's percept of B's body.*^ He supposes it rather similar to his 
own percept of B's body, but with differences of perspective. 


Places in visual space, according to our present theory, are quali- 
ties, just as colours are; therefore the total of places in A's visual 
space (apart from different excellence of vision) is identical with 
not merely similar to, the total of places in B's visual space. But 
we know empirically from perspective that the direction in which 
A sees B's body is different from that in which B sees it. Hence 
the two complexes consisting of A*s and B's percepts of B's body 
are different, both owing to differences of direction and owing 
to the differences of shape resulting from perspective. Thus when 

says "B is hot'*, he will have to describe B's percept of B's 
body (by means of the laws of perspective) and say that this is 
compresent with hotness. 

Let us consider the following stages away from present 
experience : 

(i) I am hot. 
' (2) I was hot. 

(3) You are hot. 

(4) The sun is hot 

When I judge (i), I am "aware" of a circumstance, which is 
the "verifier" of my judgment. When I judge (2), I am perhaps 
also "aware" of the verifier, though in a different sense. When 

judge (3), I am not "aware" of the verifier; still less when I 
judge (4). In (3), "hot" still means the quality I know from my 
own experience; in (4), it means an unknown cause of this 
quality, or, alternatively, the habitual coexistence of this quality 
with certain visual qualities. 

For the present, let us take "awareness" as an undefined term. 

The conception involved is the same as when 1 say that my 
hotness is part of my experience, but your hotness is not. Aware- 
ness, which we will denote by "A", is a relation which may hold 
between two events in one person's experience ; it is to be under- 
stood as including memory. In terms of A, we can define the 
person (if any) to whose biography a given event belongs. We 
do this by means of "the R-family of x'\ defined in Prindpia 



\ t 


Mctthematica *96. This may be explained in popular language 
designed to be intelligible to philosophers, as follows. 


"P" means '^parenthood'*, the P^family of x is ;c-'s ancestors 
and descendants, and brothers and sisters, and cousins in any 

degree, and cousins 

of cousins, and himself- 

provided he has 
parents or children. But if x is something having no parents or 

children, then the P-family of x is not to include x^ but to be 

the null class. In general, if R is any relation, let "S" be "R or 
its converse**. If x does not have the relation S to anything, the 
R-family of x is to be null ; but if x has the relation S to anything 


sayjK:^ let us call the journey from xtoy^xi "S-step**, Then the 
R-family of x consists of x together with all the terms that can 



be reached from ;i: by a finite number of S-steps. 

is parent, the P-family of a person x is everything that is a parent 

or child of a parent or child of ... of a:. 

Applying the above to "awareness** 


denoted by * 'A 



we may 

take awareness to consist of noticing or remembering. Thus 
X is an event in some person's biography, a:*s nearest relatives 

with respect to A will be events noticed or remembered by x 
and events which notice or remember at. If y is one of these, 
events noticed or remembered by y and events which notice or 
remember jy will be relations of x in the second degree; and so 
on through any finite number of generations. I shall call an event 
"personal" if it is aware of something or something is aware 
of it, i.e. if it belongs to the field of A. Thus if an event 
is personal its A-family contains the event itself and other 

terms, but if an event is not personal its A-family is the null 




person to 


"persons** as 

"all A-families except the null class 



We may now define "the person of x 
whom the event x belongs**, as "the A-family of x^^ 

idealist will not have to make this exception, since he will hold 
that every event is the object or subject of an awareness.) We 
can define 

which are empirical, and which have appeared in the course of 
our discussion, there is reason to believe that no two families 



the awareness-family of this'*. On grounds 



t ' 



ever have a common member, Le. that there is nothing of which 
two different persons can be aware. 

Thus "I am hot** means "hotness is a member of the awarer- 
ness-family of this, and is compresent with this**. The latter clause 


is necessary to justify the present tense "am** instead of "was, 
am, or shall be*'. The latter clause alone may sometimes be taken 
as what is meant by "I am hot'*. 
In order to understand "you are hot", we must understand 

"you**. What is **you" ? I suppose that I am seeing you (as is 
said). In that case "you** is related to an event in me, viz. the 
visual appearance of your body to me. This has a causal and also 
a perspective relation to an event in you, viz. the visual appearance 
of your body to you. The visual appearance of a human body 
to the person to whom it belongs has certain characteristic dif- 
ferences from its visual appearance to others — ^for example, it 
can contain neither eyes nor back, and the nose (if made to appear 
by closing one eye) looks more vast and portentous than to any 
one else. We can thus define two classes, one consisting of visual 
appearances of bodies to their owners, the other of visual appear- 

ances related by the laws of perspective to what I see when I 

you'*. (I am throughout assuming physics.) These two 

classes have only one common member, which is the appearance 
of your body to you. If we call this "y* *, then "you" may be 
defined as "the awareness-family of ^**. 

Thus ify is that visual appearance which (a) is related by the 
laws of perspective to what I see when I "see you**, (^) has the 
characteristics which define a body viewed by its owner, then 
"you are hot'* means "you are the awareness-family of y, and 
hotness is compresent with y'\ 

Of course if you are blind, or in the dark, or with your eyes 
shut, this definition will need to be modified. But the necessary 
modification offers no difiiculty of principle, and is therefore 

I have been assuming the theory of qualities developed in the 
discussion of proper names in Chapter VI, according to which 
there are not "instances" of hotness (or at any rate of a given 



degree of hotness), but complexes of which hotness is an element. 
Space-time, on this view, depends upon qualities which are 
empirically unique, such as those used in defining latitude and 
longitude, and the complex "hotness compresent with such-and- 
such a quality, or collection of qualities" takes the place of "hot- 
ness in such-and-such a place". This makes little difference after 
the definitions have been given. 

We come now to "the sun is hot". This may be interpreted 
in two ways. It may mean only "seeing-the-sun is usually com- 
present with feeling hot"; this is a generalization from expe- 
rience. Or it may mean, as in physics: "experiences of a certain 
sort, called sensations, have causes that are not in the experiencer j 
experiences of hotness have causes which all have a certain 
character called heat ; the causal chains that start backwards from 
the experiences called seeing- tke-sun meet in a certain region, and 
in this region there is heat". We are not concerned to choose 
between these two intrepretations, but only to consider both. 

As regards the complexes which, on my view, take the place 

of "instances" of hotness, I should use the relation "com 
presence". This relation subsists between any two things that 
simultaneously experience, e.g. the sound of a piano and the 
sight of the piano player. But I suppose that it also holds between 
any two physical events which overlap in space-time. I now form 
a group of events all compresent with each other and not all 
compresent with anything outside the group; this I call a "place 

(or perhaps a "point") in space-time. I assume the usual rules 

about places, but only as empirical generalizations — e.g. no place 


is earlier than itself, or to the left of itself, etc. Then an "instance" 
of hotness is any place of which hotness is a member. 
Starting from "this", we can define "I", "here", "now", etc 

as was done in the chapter on egocentric particulars. 

Let us now return to the question of "verifiers". If I say *' 
am hot", the verifier is an event of which I am aware, namely 
hotness-here-now. But if I say "you are hot", the verifier is 
hotness-rA^r^-now, of which I am not aware. This verifier cannot 
be any part of my reasons for believing that you are hot; these 



reasons must be derived from my experiences and prejudices. 
(Prejudice = synthetic a priori.) My reasons, in fact, must be 
derived from me. 

When I say "the sun is hot", interpreted as in physics, I travel 
further from experience, since "hot" now means, not "hotness" 
which I have experienced, but "cause of hotness", which I have 

not experienced. The verifier of 


sun IS 



is not only 

unknown, like that of "you are hot'', but unimaginable. My 
grounds for believing "the sun is hot" (interpreted as in physics) 
are thus even more remote from the verifier. 

The "verifier" is defined as that occurrence in virtue of which 
my assertion is true (or false). 

Formally, whenever an assertion goes beyond my experience, 
the situation is this: inference leads me to "there is an x such 

, and this, if 

that <l)x' 

which would be asserted by 


true, is true in virtue of an occurrence 



But I know no such occur 

When I say "I am hot", I am aware of the verifier, which is 


or "the sun is hot", I 


my hotness. When I say "you are 
am not aware of the verifier. 

In the case of "I am hot", there is a simple kind of corre 
spondence between the statement and the verifier. In this case 
the correspondence-theory of truth holds simpliciter . This case 
covers all the factual premisses of empirical knowledge. It does 
not cover the premisses used in inferring, e.g, induction. 

In all other empirical assertions, such as "you are hot", the 
correspondence on which truth depends is more complex. The 
assertion is of the form "there is an x such that ^x^\ and the 
fact" is that which, for a suitable a, would be asserted 




But we cannot make the assertion "^a" because we are not 
aware of a. 

A great deal of metaphysics is involved in the belief that I can 

make assertions, such as 


you are 

hot", which go beyond my 

experience. I cannot imagine any way of discovering whether 

the metaphysics in question is true or false, but I think it is 
worthwhile to state the assumptions involved. 





We have spoken of the assumptions as "causal," but without 
investigating what we mean by this word, which, I am convinced 
is capable of an important diversity of meanings. Let us consider 
various cases. 

First: A and B have been frequently conjoined in experience, 
therefore when I see A I expect B. This raises the problem of 
induction, but not our present problem, which is that of trans- 
cending my experience. 

Second: consider what makes me think that you have expe- 
riences that I do not have. The argument is obviously analogical, 
but is hard to state precisely. Suppose, e.g,, you say "I am hot**, 
and I infer that you are hot. When I am hot, I say "I am hot**, 
and hear certain sounds (made by myself). I hear similar sounds 

when" I am not speaking and not hot. I infer that they have a 
cause or antecedent similar to that which they have when I make 

The argument, formally, is as follows. In a large class of cases, 
I know that events of kind B are preceded by events of kind A ; 

in another large class of cases, I do not know whether this is 



the case or not. In the absence of evidence to the contrary 
assume that it is the case. This is still induction, but it differs 
from the previous kind by the fact that there can be no evidence 
for or against it, except the indirect evidence that, accepted as 
a scientific hypothesis, it leads to no untoward consequences. 

The above is the argument for the existence of other "minds 
It remains to examine the argument for the physical world. 

The simplest form of the argument for the physical world is 

^ exist when I do not see them— or 
rather, to avoid Berkeley, when no one sees them. Suppose, for 
example, that I keep my cheque-book in a drawer, so that it 
affects no one*s senses except when the drawer is open. Why 
do I believe that it is there when the drawer is shut, and even 
when no one sees the drawer } 

Some philosophers might argue that, when I say "the book is 

the argument that 




see It 



in the drawer**, I only mean "if anyone opens the drawer he will 

opening the drawer** must be interpreted as an 




i f 



experience, not as something done to a permanent drawer. This 

view, right or wrong, is one which would only occur to a philo- 

sopher, and is not the one I wish to discuss. What I wish to 
discuss is the view that something — ^which may be called the book 

is occurring when no one sees it. I do not wish to discuss 
whether the view is true, but what kind of influence is involved 

in supposmg it true 

Unsophisticated common sense supposes that the book, just 
as it appears when seen, is there all the time. This we know to 
be false. The book which can exist unseen must, if it exists, 
the sort of thing that physics says it is, which is quite unlike 
what we see. What we more or less know is that, if we fulfil 
certain conditions, we shall see the book. We believe that the 
causes of this experience lie only partly within ourselves; the 
causes external to ourselves are what lead us to belief in the book. 
This requires belief in a kind of cause which completely and 
essentially transcends experience. What is the argument in favour 

of causes of this kind ? 

The belief from which we most naturally arrive at matter is, 
I think, the belief that in sensation we are passive. We experience 
sights and sounds, broadly speaking, involuntarily. Now the 
conception of **cause'* — -however loath we may be to admit this 
fact — ^is derived from the conception of "will". Since we do not 
will what we see and hear, the cause of what we see and hear 

must, it is felt, be external to us. This is an argument which only 
has to be stated in order to be rejected. Is there any better argu 
ment for the physical world ? 

The only remaining argument, so far as I can see, is that the 
hypothesis of the physical world simplifies the statement of causal 
laws — ^not only of those that cannot be verified, but also of those 
that can. Of course there can be no argument against the physical 
world, since experience will be the same whether it exists or not. 
Therefore it is justified as a working hypothesis. But more than 
this cannot be claimed on the groimd of simplicity. 

This concludes the discussion of the relation between a singular 
bdief and dte £act in virtue of which it is true (or nilse). It 'will 



be seen that this fact is often quite remote from the grounds upon 
which we entertain the belief, and that the belief may be (in some 
sense) knowledge even when the fact is quite unknowable.^ 

The relation between belief and fact is even more remote in 


the case of general beliefs, such as "all men are mortal". Here 
there is not a single verifier, but an indefinite multitude, though 
there could be a single "falsifier". We have not yet considered 
what is expressed by such beliefs as "all men are mortal", but 
it is clear that there can be only a very remote correspondence 
between what is expressed and the multitude of verifiers. For 


the moment, I do not propose to discuss this problem; I mention 
it only in order to point out how much still remains to be 

Chapter XVII 




My purpose in this chapter is to consider the relation between 
truth and experience, or, what comes to the same thing, between 
truth and knowledge. The most important question in this con- 

nection is whether 







is a wider concept than "knowledge 
and whether a proposition which is theoretically incapable 
being proved or disproved, or rendered probable or improbable 
by means of our experience, is nevertheless true or false. But a 
good many preliminaries are necessary before we can discuss 
this question. 

"Truth", we have agreed, is a property primarily of beliefs 
derivatively of sentences. Some beliefs can be "expressed" 
sentences containing no variables — e.g. "I am hot 



which transcend the experience of the believer— e.g. "you are 



always involve variables in their expression 



beliefs whose expression involves variables do not transcend 
experience, and among these some are basic. This is most evident 

. "that book is somewhere in my 






shelves". This can be replaced, after search, by "that book is 
here^\ but in such a case as "you are hot" this is impossible. If 
I believe "something has the property/" but know no proposi- 
tion "a has the property/", I naturally suppose that, given some 

experience which I have not had, there would be a proposition 
of the latter sort describing this experience. There seems to be 
here an unconscious assumption that experience is purely con- 
templative, so that an event which I have not experienced might 
have remained unaltered if I had experienced it. 

The question of truth which transcends experience may be 

put as follows: suppose a^, a^ 


an are all the names in my 



vocabulary, and that I have named everything 

can name 

Suppose yoJi,^ 


are all false, is it nevertheless possible 

that "there is an x for which fx'' should be true ? Or, alternatively 
can I infer ''fx is false whatever x may be" ? 
We cannot discuss this tjuestion without first defining what is 






there is an x for which fx 



proposition is called an "existence-proposition 


is impossible to define 


for existence-propositions 

except in terms of basic existence-propositions. Any other 
definition will use existence-propositions. For example, in the 
above instance, "consider there is a person, other than myself, 


whose vocabulary contains some name h which mine does not 

contain, and which is such that, for him, ft is a judgment of 


perception". This is only a new and more complicated existence 


person by God 

even if, like 

Berkeley, we replace the hypothetical 

It seems, therefore, that we must enumerate basic existence- 


"true" existence-propositions as 

propositions, and define 

deducible from these. But this leaves the question: "in what sense 

are the basic existence-propositions true? It seems we shall 

have to say they are "experienced". For instance, when some one 
knocks on the door and you say "who's there?" you know 
"some one is there" and you wish to know a proposition of the 
form "a is there". 

Suppose we assert "there is an x such that /at" when, for 
every name we know, "/a" is false. We cannot, in this case, get 
a linguistic statement without a variable. We cannot say: "there 
is a name 'a such that ^a is true", for this merely substitutes 

name as 

variable, and is less likely to be true than the ori 


ginal statement. If I believe, for instance, that there are occurrences 
in the physical world which no one perceives, these occurrences 
must be nameless; the translation which substitutes a hypo- 
thetical name will therefore be false, even if the original belief 
was true. 

It is clear that, unless our knowledge is very 



limited than there seems any reason to suppose, there must be 





basic existence-propositions, and that, in regard to some of these 

every instance "/a" that we can give is fialse. The simplest 

example is "there are occurrences which I do not perceive*' 
cannot in language express what makes such statements true 
without introducing variables; the "fact" which is the verifier 
is unmentionable. 

Nevertheless, if "there is an x such that/:v" is true, it is true 
because of some occurrence, although, in the case supposed, we 
do not experience this occurrence. This occurrence may still be 
called the "verifier". There is no reason to suppose the relation 
of "there is an a: such that fx'^ to the verifier to be different 
when the verifier is not experienced from what it is when the 
verifier is experienced.* When the verifier is experienced, the 
knowledge-process is different, but that is another matter. When 
I experience an occurrence, it enables me to know one or more 
sentences of the form "/cz", from which I can deduce "there is 
an X such that/:^". This new sentence has a different relation to 
the occurrence from that which "/a" has; the relation of "/a" 

to the occurrence is only possible when a is experienced. But this 
is a linguistic fact. The relation of "there is an x such that/:v" 
to the occurrence, unlike that of "/a", does not demand that the 
verifier should be experienced. And the relation may be just the 
same when the occurrence is not experienced as when it is. 

If I am asked "what occurrence makes 'there is an x such that' 
fx* true?" I can answer by a description which involves existence- 
propositions, but I cannot answer by naming the occurrence. 
When I can name such an occurrence, I do more than is necessary 
for the truth of "there is an x such that /at", since an indefinite 
multitude of other occurrences would do equally well. If I say 
"there is at least one man in Los Angeles*', any man in Los 
Angeles will do equally well as a verifier. But when I say "there 
are invisible parts of the moon's surface", I am not acquainted 
with any verifier. 

If there are bas^c existence-propositions, as we seem driven to 
conclude, their relation to perception must be very different 


This subject will be considered further at the end of this chapter. 



from that of judgments of perception. In the case of memory, 

"that book is somewhere in my shelves", there was once a 




judgment of perception. It would be possible, though I 
think it would be right, to argue that, at the time of perception, 
inferred the existence-proposition, and now remember it. 

This would make the existence-proposition not basic. But there 
are other cases that are more stubborn. 

Take events perceived by no one. I do not want to assert 
positively that we know of such events, but to inquite what is 
involved in supposing that we do. To make the matter concrete, 
let us imagine that I am walking just outside my house when a 
tile hits me on the head, I look up, and see the place on the roof 
from which it has apparently fallen. I am quite persuaded that it 
existed before it hit me. What is involved in this persuasion ? 

It is customary to appeal to causation, and to say that from 

perceived facts I infer unperceived facts. Obviously it is on 
occasion of perceived facts that I believe in unperceived facts, 
but I do not think this is an inference. Before we see the tile we 
say ^^ something hit me", and this judgment is just as immediate 
as a judgment of perception. It would be possible, therefore, 
instead of a general principle of causal inference, to substitute a 
number of basic existence-propositions, each as immediate as 
perceptive propositions. From these, causation would be derived 

This point is not very important. On the usual view, we know 
a judgment of perception /?, and also "/? implies that there is an 
X such that/;^'*; on the view I am suggesting, when we know^ 
we know that there is an x such that fx. The difference between 
the two views is negligible. 

There is no reason why basic empirical knowledge should not 

be of the form "there is an ;c such that/^" . To know this is less 
than to know **/«". If a has the property f, it may ccatse me to 
know "there is an x such that /at" without causing me to know 


"you are hot", /is known; this therefore illustrates the 
above. In purely physical statements, such as "sound is composed 

of air- waves 



C( /*>* 

involved is not very obvious. To interpret 



such statements, we must take theoretical physics in its (at present) 
most advanced form. Where does this touch experience ? 

(i) Physical events have a space-time order correlated (not 
very exactly) with that of percepts. (2) Certain trains of physical 
events are causal antecedents of certain percepts. We may hence 
conclude (a) that time is the same in the physical as in the psy- 
chological world; (Jb) that compresence (which we know as a 
relation between any two parts of one experience) also exists in 
the physical world ; (c) that if I have two qualitatively different 
experiences, their causes have differences which in some way 
correspond. This gives the experienced elements in physical 

In any significant sentence, the constants must all be derived 
from experience. Space-time order in physics, for example, is 
derived from space-time order among percepts. If we see two 
stars close together, and the polar coordinates of the stars in 

physical space, with ourselves as origin, are (r, 0, ^), (/, B\ j/\ 

6 and d' , <f> and ^' will be respectively very nearly equal, and will 
be very nearly identical in magnitude with the angular co- 

ordinates of the visual stars in our visual space. (I say "very 

nearly" because light does not travel strictly in straight lines.) 

In pure logic there are sentences containing no constants. These, 

true, are true without any relation to experience. But such 

sentences, if knowable, are tautologies, and the meaning of 

truth" as applied to tautologies is different from its meaning 


as applied to empirical sentences. I am not concerned with the 
kind of truth belonging to tautologies, and shall therefore say 
no more on this subject. 

So far we have been considering what "there is an x such that 
fx" indicates ; let us now consider what it expresses. 

We agreed that "^ or y" expresses a state in which there is 

hesitation. Sometimes this is true of "there is an x such that/^:", 
but (I think) not always. If you find a man dead of a bullet wound, 
you judge that somebody shot him, and if you are a good citizen 
you desire to replace the variable by a constant ; in this case, there 
is doubt, as in the case of "/ or q\ But sometimes you are quite 




content with "there is an x such that fx*\ and have no wish to 
replace it by "f^". Examining footprints in the jungle, you may 
say "a tiger has been here"; in this case, unless you are engaged 
in a tiger hunt, you have no wish to replace the variable by a 

perceived constant. Or suppose I say "London has 7,000,000 
inhabitants", I shall certainly not wish to replace this by "the 
inhabitants of London are A and B and C and • . ." to 7,000,000 
terms. The interesting question is: what is expressed, in such a 
case, by the sentence in which the variable occurs ? 

Suppose some one says to me "I saw a fox in the street", and 
suppose I believe him. What does this involve as to my state of 
mind ? I may have an image of a fox, more or less vague, and 
think "he saw that". This assumes that the image occurs as repre- 
sentative, since I do not think that he saw my image. Images, in 
fact, act as symbols, just as words do. Images are usually suffi- 
ciently vague to be capable of "meaning" any member of a rather 
ill-defined class of possible or actual percepts. Such an image of 

a fox as I personally can form would fit any ordinary fox. 
serves, therefore, almost exactly the same purpose as is served 
by the word "fox". Let us, then, suppose that the words which 
I hear act upon me without the intermediary of images. When I 
hear "I saw a fox", certain kinds of action may result; what these 
are will depend upon whether I am engaged in fox-hunting or 
not. But we may say, broadly speaking, that different foxes call 
for very nearly the same actions. Therefore the heard words "I 
saw a jfox" are causally sufficient. We may put the matter as 
follows: let F,, Fo», E> , . . be different foxes, and suppose that 

calls out Ao, and so on. 




seeing ¥1 calls out the reaction A^, 




etc., are 

all complex actions; there may be a part 

which they all have in common. This common part (with obvious 
limitations) may be called out by the word "fox". When I hear 
the words "there's a fox", I understand them if they call forth 
the reaction A. (This is unduly simplified, but not in ways 
relevant to our problem.) 
This makes it clear that, as 

regards what is expressed, the 

function of variables is exactly that of general words. If we take 



a pragmatic view of "meaning", and define it in terms of the 
acts (or incipient acts) to which it gives rise, then "there is an x 
such that fx*' expresses that partial act which is common to 

"/a", yb'% "/c", etc. What is expressed by "there is an x 
such that/r*' is therefore something smaller and simpler than 
what is expressed by "/a"; moreover, it is a part of what is 
expressed by "/a *, so that whoever believes *'fa'' in fact believes 

"there is an a: such that/^" 

(The situation is a little more complicated when a man has 
verbal knowledge which he does not know how to translate into 
perceptual terms. Most men know that rattlesnakes are dangerous, 
even if they cannot recognize one when they see it. In that case, 
a percept which is, in fact, of a rattlesnake, will not produce the 
appropriate reaction until some one says "that is a rattlesnake". 
In such a case the general word is more potent than the instances 
to which it is applicable. This only means, however, that, in the 
case supposed, a man's verbal experience has outrun the ex- 
perience of the things meant by words.) 

The above theory has a bearing on the theory of analytic 
inference. An inference is defined as analytic when the conclusion 
is part of the premisses. According to what we have been saying, 
Belief in the conclusion is also part of belief in the premisses: 
whoever believes *fa" is also believing "there is an ;^ such that 
fx*\ Our theory of belief does not require that a belief should 
be expressed in words ; therefore it is not surprising if, when a 
man has one belief which he expresses in words, he also has 
others, logically connected with it, which he may not express 
in words, and may not even know that he has. 

We must now endeavour to reach more precision as regards 
the relation of a belief to its verifier when the verifier is not 

■ * 

experienced. We said above that there is no reason to suppose 
the relation of "there is an jc such ihztfx" to its verifier to be 
different when the verifier is not experienced from what it is 
when the verifier is experienced. We have now to examine and 
amplify diis statement. 

In the first place, an existence-proposition has, in general. 



many verifiers, not one only; /a, fl^ fc...^ if true, are 


Statements which are true in virtue of different verifiers, each of 
which is a verifier of "there hs-dxix such that/:!c 

In the second place, when no verifier is experienced, there is 
no sentence "/a'' corresponding to an occurrence which verifies 

"there is an x such thatyV;"; this is merely because, 
thesi^ there is no such name as a. When * jTa" expresses a judg- 
ment of perception, we can distinguish two steps : first, from the 
percept to the sentence "/a'*; second, from the sentence "/a" 
to the sentence "there is an ;«• such that fx^\ There are not 
these two steps in the case supposed. It may be that "there is an 
X such that/;\r" is a basic proposition; it may be that it is a pro- 
position which is true but cannot be known. These cases must 
be treated separately. 

Take first the case in which "there is an x such that/:^:" is a 
basic proposition. Is there any reason why this should not itself 
express a fact of experience, just as *y*a** may } The word "ex 
perience" is somewhat vague; perhaps it can only be defined 

in terms of basic propositions. A coroner's Court may decide 
that A was killed by B, or that he was killed by some person or 
persons unknown. The latter conclusion is based upon a number 
of propositions either proved in Court or generally accepted; 
among these, it is logically necessary that there should be at least 
one existence-proposition. In practice, the process is more or 
less as follows: we have judgments of perception, "this is a 
bullet", "this is in the brain", and a general proposition "bullets 
in brains imply the firing of guns". This last is not a basic pro- 
position, but an inductive generalization. An inductive generaliza- 

tion is of the following form : * 'whatever x may be, fx implies 
that there is ay such that gy". The observed premisses of this 




generalization are of the form: fa ^gcL^fh.g h\fc . g c\ etc. 
where a, a\ b^ b\ c, c' are respectively simultaneous. In a new 
case we find fd^ but we do not find any d' such that g d'; we, 
however, infer "there is a simultaneous y such that^y 

There is here a distinction between inductive inference in 
logic and inductive inference as an animal habit. In logic, we 



proceed, via the inductive principle, from fa -ga\fb.g V 
fc . g c'y etc., to "whatever x may be, /at implies diat there is a 
simultaneous y such that gy'\ We then add the observed premiss 
fdy and conclude that in this case there is a y such that gy. But 
induction as an animal habit proceeds quite differently. The 

animal experiences\ fh .gb\ fc.gc' . .. and fd. 
On occasion of experiencing fd^ he believes "there is now a y 
such that gy\ but he is unaware of the causes of his belief. 
When, in die course of evolution, he becomes an inductive 
logician, he notices the causes and says they are grounds. Since 
they are not, he might just as reasonsdjly accept "there is now a 
y such that gy** as a basic proposition; it is simpler than the 
inductive principle, and also more likely to be true. In this 
respect, therefore, the animal is to be preferred to the logician. 
This is a vindication of Hume. 

However this may be, we must, I think, concede that there are 
existence-propositions that are basic. They have a correspondence 
with fact, though this is not of quite the same kind as in the case 
of propositions not containing variables. If "/a" is a basic pro- 
position, the fact corresponding to it is 4ts cause. Now the belief 
"there is an x such that/;v" is part of the belief "/a*', when 
the latter belief exists ; when it does not, the fact has had only 
part of the effect required to produce the belief "/fl", najnely 
that part which produces the belief "there is an x such 
that /at". The reason may be merely that the causal chain 
from fact to belief is longer than when the fact causes the 
beUef yd\ 

The correspondence of truth and fact, here, is still causal, and 
of the kind connected with "meaning" or "significance". 

We now have to ask ourselves: is there a sense in which a 
proposition may be true although it cannot be Jknown } Take, 
say, "in the invisible part of the moon there is a mountain of 
which the height is between 6,000 and 7,000 metres". Common 
sense would say unhesitatingly that this proposition is either 
true or false, but many philosophers have theories of truth which 
make this doubtful. 



Let US call our proposition S. The question is : what, if any- 
thing, can be meant by the sentence : "S is true" ? 
We may say that S is probable^ because there are such mountains 


on the part of the moon that we can see. But probability is a 
different concept from truth, and I see no reason why what is 
probable should be either true or false, unless we can define 
truth independently of probability. 

We cannot say that S is not significant, for it is correctly con- 
structed out of terms of which we know the meaning. This is 
obvious, since, if we substitute "visible" for "invisible", the 

, »««.^.>., 

sentence becomes one asserted by astronomers; and "invisible" 
means "not visible" and no sentence is deprived of significance 
by the insertion of the word "not". 

Common sense imagines travelling round the moon (which 
is only technically impossible), and holds that, if we did so, we 

should either see or not see the mountains in question. It is 
because of imagining itself a spectator that it is so sure of 
being significant. The astronomer may say : mountains on the 
fiirther side of the moon would have gravitational effects, arad 
might therefore conceivably be inferred. In both these cases, we 
are arguing as to what would happen in the event of a hypothesis 
which has not been verified in our experience. The principle 
involved is, in each case: "in the absence of evidence to the 
contraryj we shall assume the unobserved portions of the uni- 
verse to obey the same laws as the observed portions". But 
unless we have an independent definition of truth concerning 
what is unobserved, this principle will be a mere definition, and 
the "unobserved portions" will be only a technical device, so 
long as they remain unobserved. The principle only says some- 
thing substantial if it means "what I shall observe will be found 

to resemble what I have observed", or, alternatively, if I can 
define "truth" independently of observation. 

On what may be called the realist view of truth, there are 
"facts", and there are sentences related to these facts in ways which 
make the sentences true or false, quite independently of any way 
of deciding the alternative. The difficulty is to define the relation 




which constitutes truth if this view is adopted. The question is 

seriouSj since, as we have seen 

it is not only such things as the 
further side of the moon that are unobserved, but also cats and 
dogs and human beings other than ourselves. 
A sentence which is true in virtue of an unobserved fact must 

contain at least one variable. The sentence 



are men in 

Semipalatinsk* ' is true in virtue of particular facts, but as I do 
not know the name of any inhabitant of that region, I cannot 

r, has 

adduce any of these fects. Each of these facts, howeve 


determinate relation to my sentence, and each has the same 

: the 

relation to it. I do not think there is any real difficulty; 
apparent difficulty is due to the trivial circumstance that what has 

no name cannot be mentioned. I conclude, therefore, that sen 

tences containing variables may be true in virtue of a relation to 
one or more unobserved facts^ and that the relation is the same 


as that which makes similar sentences true when they concern 
observed facts, e.g. "there are men in Los Angeles". Unobserved 
facts can be spoken of in general terms, but not with the par- 
ticularity that is possible where observed facts are concerned. 

And there is no reason why 
conception than "knowledge". 



» o 

should not be a wider 



Chapter XVIII 



We have been concerned Ktherto with beliefs as to particular 
matters of fact, when these result as directly as possible from 
perception ; we have considered also, though less fully, beliefs in 
the verbal expression of which the word "some" occurs, which 
we found important, especially, in connection with memory 
We have now to consider beliefs in the verbal expression of which 
either the word "all" or the word "none** occurs. As hitherto, 
I shall confine myself to extra-logical beliefs. 

There is, in all such inquiries, a combination of logic and 
psychology. Logic shows us the goal we have to reach, but psy^ 
chology must show us how to reach it. Our psychology of belief, 
while it must be able, af it§ conclusion, to embrace the refined 
abstractions of the logician, must, at its outset, be applicable 
to animals and young children, and must show logical categories 
as a natural development out of animal habits. In this we are very 
much helped by our decision that belief is essentially pre-linguistic, 
and that, when we express a belief in words, we . have already 
taken the most difficult of the steps that lead from the animal to 

the logician. 

The psychology to be offered in this chapter, as in previous 
chapters, is more or less schematic, and is not asserted to be 
correct in detail. What is asserted is that something of the general 
kind that is suggested is necessary in order to pass from animal 
habits to what logic demands. Accuracy as to the detail is matter 
for the psychologist, and must depend upon investigations some- 
what remote from theory of knowledge. So far as psychology is 
concerned, I am content if I can persuade the psychologist of 
the nature and importance of the problems that I indicate. 




General beliefs— by which I mean such as, in their verbal 



involve "all'* or "none" or some synonym 

their pre-intellectual origin in habits of a certain kind. In those 
who possess language, such habits may be purely verbal. The 

' may suggest the word "yellow"; the word 





may suggest the word "twelve'*. Scholastic education 


produces a mass of knowledge of this sort, which may be almost 
wholly unrelated to what the sentences employed signify. We 
however, are in search of something pre-linguistic, and must 
therefore, to begin with, ignore habits concerned with words. 

Consider the behaviour of a dog. When he sees his master 
put on a hat, he expects to be taken for a walk, and shows his 
expectations by leaps and barks. A certain smell suggests rabbit; 
so does a rabbit-hole, or any place where he has frequently found 
rabbits. The smell of a female on heat will stimulate incredible 

exertions. I am told that horses are terrified by the smell of a 
bear-skin even if they have never seen a bear. The above kinds 
of behaviour are partly instinctive, partly the result of experience. 
The smell of a rabbit or a female has an instinctive effect, but the 
master's hat has an effect generated hf previous occurrences. In 
both kinds of cases alike, if the dog were miraculously endowed 

-■ ■ 

with language and the mental habits of a philosopher, he would 
be led to enunciate a general proposition. He would say "where- 



is this smell, there 

is something edible", and "my 

master's putting on his hat is an invariable antecedent of his 

going out". If you asked him how he knew this, he would say 
in the latter case, that he had observed it 


and in the former, that 
it was a synthetic a priori intuition. He does not say this, because 
he cannot talk; but we say very similar things in very similar 

Let us consider some rather easy general propositions, such as 
"any neighbourhood that contains a smell of a certain sort also 
contains bacon". Let *y}v" mean "there is a certain kind of smell 
in the neighbourhood x'\ and let "gx*' mean "there is bacon 


in the neighbourhood x*\ Whenever we eat bacon, we ex- 
perience both fx and gx^ and when we experience fx alone we 



usually find that, by a suitable efFort, we can arrive at also ex- 
periencing gx. This state of affairs in time generates a habit of 
believing gx whenever we believe fx. So far, however, we are 
not believing any general proposition. The psychologist who 
observes us can arrive at a general proposition: "whenever 
Mr, So-and-so believes fx^ he also believes gx'' But this is not 
the general proposition we want, which is "whenever fx is 
true, gx is also true". For Mr. So-and-so, however, this latter 
general proposition results from his observation, exactly as the 
psychological proposition results from the observation of the 
psychologist. Whatever is to be said for or against the one general 
proposition is to be said equally for or against the other. 

Let us try to consider in more detail the proposition "when- 
ever there is fx there is gx'\ Consider, first, the various values 

of the function f say /<2, fb^ fc^ . . . Each of these is a pro 

position which can be believed: /a, for instance, says "the 
neighbourhood a has a certain smell (that of bacon)'*. The 
smell is strictly a class of smells, since two pieces of bacon do not 
smell exactly alike. Let us call the class of smells in question a, 
and the class of bits of bacon j3. Or, to avoid the assumptions of 
physicalism, let j3 be the class of visual perceptions called "seeing 
bacon". We may somewhat alter our original proposition so as 
to simplify our discussion; we can take it as saying "whenever 

I smell bacon, I see it then or soon afterwards". To make this 
precise, let us fix on a time-interval t which we consider short 
say five minutes. Then our statement becomes: "whenever a 
member of the class <t occurs, there is a slightly later member of 
the class j8, such that the time-interval from a to j3 is less than 
r", where t is a given constant time-interval. This is rather com- 
plicated; let us see whether anything simpler is possible. 

When I begin my reflections, I observe that, on certain specific 
occasions, I have experienced fa and expected ga, experienced 
fb and expected gb, etc. I observe also that my expectations have 
not been disappointed. The time t which appeared in our previous 
statement is now replaced by the time taken for an expectation to 
be disappointed. This of course varies with the character of the 





analogue of memory, and not to cover any belief about the 

Animal induction differs from scientific induction in various 
ways ; one of these is that the former, but not the latter, involves 
expectation. When, in the experience of an animal, an event of 
kind A has been quickly followed by an event of kind B, if B is 
emotionally interesting the animal comes to expect B whenever 

occurs. How many experiences are necessary depends upon 
the degree of emotion aroused by B ; if B is very pleasurable or 
very painful, one experience may suffice* As soon as the animal 
has acquired the habit of expecting B when it sees A, it behaves, 
in the presence q/* -^, as a man would who believed the general 

proposition "A is always followed by B". But the animal is at 
no time believing anything that can only be expressed in words 
by mentioning both A and B. It sees A, and it expects B ; these 
two, though we see them to be causally connected, are separate 
beliefs in the animal. We, when we reflect upon our own animal 
behaviour, may observe that A has always hitherto been followed 
by B, or we may observe the two laws "A causes expectation of 
" and "expectation of B is followed by B". These two laws will 
begin to be true at a later time than our first experience of the one 
law that A is followed by B, since a certain number of experiences 
of the one law are necessary to cause instances of the law that A 
causes expectation of B. Ajny one of the three laws may fail at 
any moment, but I am considering the case in which this does not 


The importance of the above is that it shows the limitations 
of animal induction. This never leads to belief in the general 


proposition "A is followed by B", but only, when A occurs, to 
the expectation "B will occur". Belief in general laws, however 
inductive and however mistaken, requires a higher intellectual 
development than is required for what may be called "inductive 
behaviour" in the presence of the stimulus A. Speaking prag 
matically, there is the essential difference that belief in the general 
law, as opposed to animal habit, can influence action in the 
absence of the stimulus A. 



In a scientific induction, expectation in the above limited sense 
is not involved. Take one of the earliest of such inductions the 
Egyptian discovery of the periodicity of eclipses. Here the events 
foretold were too distant to be "expected" in the physical sense. 
In a scientific induction, two events A and B are observed to occur 
together or in close temporal succession, but no physical expecta- 
tion is generated, or if it is, it is regarded as irrelevant. The 
hypothesis that A is always accompanied or followed by B pre- 
cedes the helkfiibzt this is the case, and the belief never acquires 
the dogmatic and immediate quality of animal expectation. I 
cannot help thinking, however, that our obstinate belief in 
induction has some connection with animal expectation. But this 
is a purely psychological question, of no essential importance to 

our inquiry. 

We must now attempt to analyse what is "expressed" by the 
words "A is always followed by B". What is expressed cannot be 
merely that, when I experience A, I expect B, for this is another 
general law, which would have to be similarly analysed, and we 
should thus be led into an endless regress. What is expressed 

must be a belief involving both A and B, not a merely causal 

relation between a belief involving only A and another belief 
involving only B. 

Suppose I am believing that all men are mortal, what sort of 
thing must be occurring in me } I think that a belief of this kind 
is sometimes affirmative, sometimes negative, where these terms 

are to be interpreted psychologically. A belief is affirmative 
when what is considered is accepted, and is negative when what 
is considered is rejected. Thus "all men are mortal", when 
affirmative, will involve some connection between the predicates 
"man" and "mortal", but when negative may be represented by 
the question "an immortal man .^" followed by the answer "no". 
The psychology is somewhat different in these two cases. Let us 
take the affirmative first. 

It might be thought that "whatever is human is mortal" could 
be interpreted, on the subjective side, as only a relation between 
the two predicates "human" and "mortal". We might say: the 





beliefs "A is human", "B is human'Vetc, all, considered as events 
in the believer, have something in common; this something is 

what is "expressed*' by the predicate "human". Similarly there 
is something "expressed" by the predicate "mortal". We might 
be tempted to say that one of these predicates implies the other, 
and to use this as an analysis of what is "expressed" by "all men 

are mortal". 
This Aristotelian interpretation, however, overlooks the fact 

that the connection is not between the predicates as such, but only 

between the predicates as predicated of one subject. "A is human" 

involves "A is mortal", but not "B is mortal". We cannot there- 

fore eliminate the hypothetical subject and the hypothetical pro- 
positional form in interpreting "all men are mortal". 
When I believe "all men are mortal", I believe, if I am a logician, 
for all possible values of x^ if x is human x is mortal". It is not 

the case that, for all possible values of x^ I believe that if x is 
human x is mortal. For if this were the case, I should have as 
many beliefs as there are possible values oix^ and if a is a possible 

value of x^ I should be believing "if a is human, a is mortal 

But I may have never heard of c, and therefore be incapable of 
this belief. Thus the belief that all men are mortal is one belief 


and the generality is part of the belief. Moreover, it is intensional 
in the sense that I can have the belief without knowing all the 

men there are. As soon as I understand the words "human 
and "mortal", the subject-predicate form, and the "if-then 

form, I have everything, except generality, that is required for 
understanding "all men are mortal". 

We have already seen that general propositions cannot be 
explained as habits, although they are genetically connected with 
habits. This is obvious for three reasons. First : a general pro- 
position is required in order to state that a given person has a 
given habit; we have to be able to say "Mr. A always responds 
to stimulus A by the action B". If, therefore, we attempt to use 
habit to explain general propositions, we shall be involved in 
an endless regress. Second: general propositions not only can 
be understood, but can influence our actions, in the absence of 



the Stimulus to the associated habit. Suppose I believe **all wild 
giraffes live in Africa", that does not mean merely that whenever 
I see a wild giraffe I diink "I must be in Africa"; it means also 

that, when I am thinking of starting on a big-game hunti 


expedition, I think "if I want to hunt giraffes, I shall have to go 

to Africa". Third: when I discover a general proposition by 

scientific methods, the knowledge that I obtain ante-dates any 
habit connected with it. The belief that metals conduct elec- 
tricity may generate a habit, but was not generated by a habit. 

In order to make any further advance in the analysis of what 
is "expressed" by a general proposition, we must, I think, adopt 
the alternative interpretation, mentioned above, in which the 
proposition is interpreted as denying an existence-proposition. 
"No A is B" denies "Some A is B"; "All A is B" denies "Some A 
is not B", Thus from this point of view "No A is B" is simpler 
than "All A is B". We will therefore consider it first. 

In connection with factual premisses, we considered the man 
who is asked "do you hear anything?" and replies "No, I hear 
nothing". This man, we said, has committed himself to the 
stupendous generalization: "everything in the universe is not a 
sound now heard by me". However true this may be as regards 
what is "indicated", it is impossible to believe that it is true of 
what is "expressed". Let us see whether we can arrive at a less 
unplausible interpretation of what is "expressed". 

Consider a series of judgments of perception "I hear A", *' 
hear B", "I hear C", etc. These all have something in common 
namely a stimulation of the auditory centres and a certain kind 
of sensation. What they all have in common is what is meant by 
the word "hear". This is expressed by "I hear something", which, 
on the side of expression, is simpler than "I hear A". 

We saw in an early chapter that there are two kinds of affirma- 
tion: one of these belongs to judgments of perception, occurs 
only in the 'object-language, and has no correlative negation ; the 
other, which can only occur in languages of higher order, arises 
when a proposition is first considered and then accepted. This 
second kind has a correlative negation, when the proposition, 






after being considered, is rejected. Rejection of a proposition is, 
psychologically, inhibition of the impulses which belief in the 
proposition would generate ; it thus always involves some tension, 
since the impulses connected with belief are not absent, but are 
counteracted by an opposing force. 

Let us apply this to the man who gives a negative answer to 
the question whether he hears anything. We have already seen 
what is expressed by "I hear something". The question causes 
the man to consider this proposition, and after considering it he 
rejects it; he expresses his rejection in the words "I hear nothing". 
This seems an intelligible and psychologically credible account 
of what happens in such a case. 

In the case of an affirmative general proposition, "All A is B", 
there is an extra complication, but no new difficulty of principle. 
Let us take again "all men are mortal". This is to be interpreted 
as "are some men not mortal? No". The process may be ampli- 
fied as follows. When we judge "A is a man but not mortal", 
we accept "A is a man" but we reject "A is mortal". The various 

acts of this kind, putting B, C, etc., in place of A, all have some- 
thing in common ; what they have in common is a belief expressed 
in the words "some man is not mortal". When we reject this 
belief, we are in a state expressed by the words "all men are 


mortal". These words thus express a double negation, or, speaking 
psychologically, the inhibiting of an inhibition. So far as 
remember, pre-verbal forms of this operation were studied by 

Pavlov in dogs. 

We must now inquire into what is "indicated" by a general 
belief, and how, if at all, we can know that a general belief is true^ 

As regards what is "indicated" by a general belief, we must 

remember that, as we saw in an earlier chapter, the world can, in 
theory, be completely described without the use of any logical 
words. "Had we but world enough and time", we could dispense 
with general propositions. Instead of "all men are mortal", we 
could say "Socrates ia mortal", "Plato is mortal", and so on. In 
fact, however, this would take too long, and our vocabulary of 
namies is insufficient. We must therefore use general propositions . 




But the subjective character of logical words appears in this 

that the state of the world which makes a general proposition 


true can only be indicated by means of a general proposition. 
If "all men are mortal" is to be true, there must be an occurrence 
which is A*s death, another which is B's death, and so on through- 
out the catalogue of men. There is nothing in the world which 

', and therefore there is no one verifier of 





all men are mortal". 
According to modern logic, "all men are mortal" is a state- 
ment, not only about men, but about everything. This is certainly 
a possible interpretation, and certainly the most convenient for 
logic. But it is difficult not to believe that the statement can be 
interpreted so as to be only about men. Let us examine this 

If I wish to make "all men are mortal" a statement which is 

only about men, I must first have an extensional definition of 




"A, B, C 

is a complete list 


\ Then, in order to prove that all men have a certain pre- 
dicate, I need only observe that this predicate belongs to A and 





the rest of' the universe is irrelevant 

This is all very well if men are a conventional collection; but if 
"men" are defined as those objects which possess a certain pre- 
dicate, how am I to know that my list A, B, C 

IS com 

plete } In fact, in the case of men, I know that any list that can 
be framed is incomplete. This, it may be said, is merely due to 
my limitations; an omniscient Being could be sure that the list 
is complete. Yes, but only in virtue of knowledge about every- 
thing: He would know, concerning each thing outside the list, 
that it was not human, and this knowledge would be essential.' 



however, does not seem 

quite conclusive. Ignoring 

means of knowing, let us suppose that, in fact, A, B, C . . . 
are all the men there are, and let us suppose that there are occur 

♦ • f 

rences correctly described as A*s death, B's death, C's death, 
Z*s death. Then, in fact, it is true that all men are mortal. Thus 
the number of occurrences required to insure the truth of "all 
men are mortal" is the sanae as the number of men, and no more. 




Other occurrences are necessary in order that we may know our 

list to be complete, but not in order that it may be complete. 
We may conclude, therefore, that the occurrences required to 
make a statement about all men true are as numerous as men, 
but not more numerous. These occurrences collectively are the 
verifier of the statement in question. 

Let us consider some case where we seem more certain of the 
truth of our general proposition, say "all dodos are mortal". 
We know this, it may be said, because all dodos are dead, 
might be objected that perhaps there are dodos in other planets, 
or that evolution, having produced the dodo once, may produce 
it again, and next time may make it immortal, like the phoenix. 
We will therefore amend our general proposition, and say only : 
"all dodos living on the surface of the earth before 1940 were 
mortal". This seems fairly indubitable. 

The proposition at which we have now arrived is strictly 

analogous to "there is no cheese in the larder", which we con- 
sidered at an earlier stage. It requires, for its proof, a survey of 
the earth's surface, leading to a set of negative propositions of 
the form "this is not a li-^ing dodo", applied to every terrestrial 
portion of space-time large enough to have any chance of being 
a dodo. These negative propositions, as we saw, depend upon 
negative propositions such as "this is not blue". The generality 
is strictly enumerative, and is rendered possible by the fact that 
our defining predicate contains a space-time determination, 
is the peculiarity of such predicates that, given favourable cir- 
cumstances, they can be shown empirically to be equivalent to a 
list. But that this is empirically possible is itself an empirical 
fact, connected with the properties of space-time which we con- 
sidered in cormection with proper names. 

According to the above, what is "indicated" by a general 
statement of the form "All A's are B's" is a collection of occur- 

of the 

rences, one for each A. This 

collection is the "verifier" 

general statement : when every member of the collection occurs, 
the statement is true ; when there is any member of it that does 

not occur, the statement is false 




We come now to the question how, if at all, we can know 
empirical general propositions. We have seen that some among 
such statements can be known by means of a census ; this happens 
when the objects concerned are confined by definition to a region 
of space-time which is in our neighbourhood and none of it in 
the future. But this is an exceptional case, and probably, when 
our knowledge of space- time is adequately analysed, will be found 
to be ultimately no real exception. Certainly in all other cases it is 
impossible for us to know that we have made a complete census, 
and our knowledge of a general proposition must therefore, 
it exists, be obtained by other methods. 

think that, if we are to be allowed to know any empirical 
generalizations except those derivable from a census, the word 
"know" will have to be used rather more liberally than hitherto. 
We could be said to "know" a proposition if it is in fact true and 
we believe it on the best available evidence. But if this evidence 
is not conclusive, we shall never know whether the proposition 
is in fact true, and shall therefore never know whether we know 

it- It is hoped that inductive evidence may make an empirical 
generalization probable. This takes us, however, into a region 
that lies outside the scope of the present work, and I shall therefore 
say no more on the subject. 




Chapter XIX 


The analysis of such propositions as "A believes p^\ "A doubts 
'' etc., raises two problems of great logical importance. In 

general, in these chapters, I have kept silent on logical topics 


but in the present connection they are unavoidable. A brief 
excursion into logic is therefore necessary before we can return 

to our main theme. 

The two logical problems that arise in connection with pro- 
positional attitudes are that of extensionality and that of atomicity. 
Of these, the former has been much discussed by recent logicians, 
while the latter has been almost wholly ignored. 

Before stating the "thesis of extensionality"^ as it is called by 

Camap, it is necessary t6^say something about the theory of 
truth-functions and about the theory of classes.* The theory of 
truth-functions is the most elementary part of mathematical logic, 
and concerns everything that can be said about proposi .jns by 
means of "or" and "not". Thus "/ and 5-" is the negation of 


"not-/? or not-y". The most general relation between p and 
which allows us, given/?, to infer y, is "not-/? or q\ Or suppose 
you want the most general relation which, given p and y, will 

enable you to infer r, this will be "not-/? or not-j- or r". The 
law of excluded middle is "/? or not-/?" ; the law of contradiction 

is the negation of "/ and not-/?". Two propositions are said to 

be "equivalent" when both are true or both are false, i.e. when 
we have "either/? and y, or not-/? and not-j". Two propositions 
which are equivalent are said to have the same "truth-value". 
Instead of starting with "not-/?" and "/? or q' we may start 

* In what follows I shall repeat, in a somewhat more elementary form, some 
things already said in Chapter XIII, Section C . 



with a single undefined function "/) and q are not both true" 


We denote this by "/? | ^" and call it the stroke-function. It 
obvious that "/? | p" is equivalent to "not-/', for if p and p are 

not both true, then jt? is not true, and vice versa. Again: * je? or j" 
is equivalent to "not-/? and not-y are not both true", i.e. to 


p and ? I y are not both true", i.e. to ^\p \p)\{q\ g)". Thus 

"or" and "not" can be defined in terms of the stroke-function. 
It follows that everything that can be defined in terms of "or" 
and "not" can be defined in terms of the stroke-function. 

is evident, and easily proved, that, given any proposition 
built up out of other propositions by means of the stroke, its 
truth-value depends only upon the truth- values of the constituent 
propositions. This follows from the fact that "p and q are not 

both true" is true if/? is false and also if q is false, and is false if 
and q are both true; what propositions p and g may be is 

irrelevant, so long as their truth-values are unchanged. Functions 
of which this holds are called "truth-functions". All the functions 
required in the theory of deduction are truth-functions. 

The first part of the principle of extensionality, the truth or 
falsehood of which we are to examifie, says that all functions 
of propositions are truth-functions, i.e- that, given any statement 
which contains as a part a proposition /?, its truth-value is un- 
changed if we substitute for p any other proposition q having 
the same truth-value as p. 

come now to "propositional functions". A "prepositional 
function" is an expression containing one or more undetermined 
constituents ^jkt, jy, . . . , and such that, if we settle what these are 
to be, the result is a proposition. Thus "or is a man" is a proposi- 
tional function, because, if you decide on a value for x^ the result 
is a proposition — z true proposition if you define that x is to 
be Socrates or Plato, a false proposition if x is to be Cerberus 
or Pegasus. The values for which it is true constitute the class 
of men. Every propositional function determines a class, namely 
the class of values of the variable for which it is true. 

Two propositional functions are said to be "formally equiva 

lent" if, for every possible value of the variable, the resulting 



propositions are equivalent. Thus "jc is a man" and "at is a feather- 
less biped" are formally equivalent; so are ''x is an even prime" 
and ''x is a real cube root of 8". When two prepositional functions 
are formally equivalent they determine the same class. 

Predicates may be identified with propositional functions with 
one variable, dyadic relations with those with two, triadic rela- 
tions with three, etc. When 


humans are mortal 


means "if x is human, x is mortal, for all possible values of x""* 
It is obvious that, if humans are mortal, so are featherless bipeds 
It is obvious also that, if there are n humans, there are n feather- 

less bipeds. These propositions illustrate the fact that, if two 
propositional functions are formally equivalent, a great many 
statements that are true of either are also true of the other. The 
second part of the principle of extensionality states that this is 
always the case, i.e. that, in any statement about a propositional 
function, any formally equivalent function may be substituted 
without changing the truth-value of the statement. 

Carnap states the "thesis of extensionality" in a somewhat 
weakened form, which, slightly simplified, may be enunciated 
as follows : it is possible t<3 ponstruct a language, into which any 
statement in any language can be translated, and having the 
following two properties: (i) if a proposition p occurs as part 
of a larger proposition y, the truth- value of q is unchanged if 


we substitute for p any proposition having the same truth-value 
(2) if a propositional function occurs in a proposition, the truth- 
value of the proposition is unchanged by the substitution of any 
formally equivalent propositional function (i.e. one which is true 
for the same values of the variable). 

Camap's innovation is to state the principle, not as one which 
must be true in any language, but as one which is true in a 
certain possible language into which all statements in other 
languages can be translated. 

The first of the two properties asserted by the principle implies, 
for instance, that any true statement of which "Socrates is mortal" 
is a part will remain true if we substitute "Anglesey is an island", 
and any true proposition of which **Homer was an Irishman" 



is a part (for instance, "if Homer was an Irishman FU eat my 
hat") will remain true if we substitute "Brian Boru was a Greek". 
The second property implies that, wherever the words "human 
beings" occur, we can substitute "featherless bipeds" without 
affecting the truth or falsehood of what is said— assuming that 
in fact, the class of human beings is identical with that of feather- 
less bipeds. 

Prima facie^ the thesis of extensionality is not true of pro- 
positions asserting propositional attitudes. If A believes />, and 
p is true, it does not follow that A believes all true propositions 
nor, if p is false, does it follow that A believes all false proposi- 


tions. Again: A may believe that there are featherless bipeds 
that are not human beings, without believing that there are human 
beings who are not human beings. Consequently those who 
maintain the thesis of extensionality have to find some way of 
dealing with propositional attitudes. The thesis is sought to be 
maintained for several reasons. It is very convenient technically 
in mathematical logic ; it is obviously true of the sort of state- 
ments that mathematicians want to make; it is essential to the 
maintenance of physicalism and behayiourism, not only as meta- 
physical systems, but even in the linguistic sense adopted by 
Camap. None of these reasons, however, gives any ground for 
supposing the thesis true. The grounds that have been given for 
supposing the thesis true will be examined shortly. 

The thesis of atomicity is stated by Wittgenstein as follows 
(TractattiSy 2.0201): "Every statement about complexes can 
analysed into a statement about their constituent parts, and into 
those propositions which completely describe the complexes." 
The rele^qince of this thesis to the analysis of propositional atti- 
tudes is obvious. For in "A believes/?",/? is complex; therefore, 
if Wittgenstein's principle is true, "A believes/?", which appears 
to be a statement about the complex /?, must be analysed into 
a statement ?ibout the parts of p together with propositions de- 
scribing p. Put more loosely, this means that / as a unit does not 
enter into "A believes /?", but only its constituents enter in. 

The thesis of atomicity has a technical form, and it is important 




to logic to know whether, in this form, it is true. Certain pre- 
liminary explanations are necessary before this technical principle 
can be stated. 

The object-language, as we saw, contains a certain store of 
proper names, predicates, dyadic relations, triadic relations, etc. 
Any n-adic relation can be combined with any n proper names 
(which need not all be different) to make a proposition. 

Suppose %, ngi) ^23, . . . are proper names, Pj, Pg, P3 ... are pre- 

dicates, Ri, R2, R3 . . • are dyadic relations. Si, Sg, S3 are triadic 
relations, etc. 

Then Pi {ih) stands for "/Zj has the predicate Pi** 

Ri (72i, «2) stands for "% has the relation Ri to n^^ 

1 (%> '^j ^ stands for "/Zj, n^, nj (in that order) stand in 
the relation Si**, and so on. 

All the propositions obtained in this way are called "atomic 

Now let us take any two atomic propositions p and j, and 
combine them by the stroke, so as to obtain p \ q. The proposi- 
tions so obtained, together with atomic propositions, give us an 
enlarged total of propositions. If we combine any two of this 

enlarged total by means of the stroke, we obtain a still larger 
total. Let us go on in this way indefinitely. The whole set of 
propositions so obtained we call "molecular propositions**, 
because combinations of atomic propositions compose them in 
more or less the kind of way in which combinations of atoms 
compose molecules. 

Having now reached the assemblage of molecular propositions 
by means of the sole operation of the stroke, we introduce a new 
operation for constructing propositions, which is called "gene- 
ralization**. Take any atomic or molecular proposition which 

contains some constituent a, and let us call it <^a. The same 

proposition with b substituted for a will be called ^3, and, if c 
is substituted, <f>c. Let us substitute for a not some definite term, 
but a variable x. We thus obtain a propositional function jix. 




It may happen that this is trae for all possible values of x; again 
it may happen that it is true for at least one value of x. The 
propositions asserting that either of these is the case are two new 
propositions. If they contain a constant constituent i, we can 
apply generalization in turn to iy and so on until no constants 
remain. Take, e.g., "if Socrates is a man, and all men are mortal 
then Socrates is mortal". This is not a proposition of logic 

because it mentionis Socrates and man and mortal, whereas pro 



positions of logic mention nothing particular. It is also not a 
molecular proposition, because it contains the word "all*'. It is 
on the road from a molecular proposition to a proposition 
logic. The latter is: "whatever x, a, and ^ may be, if jc- has the 
predicate a and everything that has the predicate a has the pre- 
dicate j8, then x has the predicate jS**. 

To show in detail the process of generalization involved, let 
us consider the following statement: "either Socrates is human 
but not mortal, or Socrates is not human, or Socrates is mortal". 
This is a logically necessary molecular proposition. Now when 
a proposition is true of Socrates, it is true of some one. There- 

fore the above statement remains trvie if, the first time that 
"Socrates** occurs, we substitute "some one" for "Socrates". 

(We might make this substitution for either of the other occur- 
rences, for any two, or for all three ; but the first alone suits our 
present purpose.) We thus arrive at the following proposition: 
"there is some one who has the property that either he is human 
but not mortal, or that Socrates is not human, or that Socrates 
is mortal"* (The some one in question, we happen to know, is 
Socrates, but we are ignoring this piece of knowledge.) We now 
divide the proposition a little differently, and say "some one is 
human but not mortal, or Socrates is not human, or Socrates is 
mortal". Here we have three alternatives; therefore if the first 
is false, one of the other two must be true. Now if "some one 
is human but not mortal" is false, then "all men are mortal" is 
true. Thus we arrive at "if all men are mortal, then either Socrates 
is not a man or Socrates is mortal", which is equivalent to "if 
all men are mortal, then if Socrates is a man Socrates is mortal", 



We have reached this point, from our original molecular pro 

position, by using once the process of putting "some one" in 
place of "Socrates'*, which is the logical process by which, given 
that a has some property a, we infer "something has the 
property a". 

So far, the new propositions that we have manufactured have 
been logical consequences of the earlier ones. From this point 
on, however, we are concerned with processes of manufacturing 
propositions which are not logical consequences of those from 
which they are derived. Our last statement still contained three 
"constants", namely "Socrates", "man", and "mortal". To each 
of these we apply the process of generalization, substituting x 

r Socrates, a for man, and j8 for mortal, and asserting the 
result for all values of the variables. We thus obtain "for all 
possible values of at, a, jS, if all a's are jS's, and x is an a, then x 
is a j3". This is a proposition of logic, of which our original 

proposition was an instance. But the point in which I am in- 
terested at the moment is not that we have arrived at a true 
proposition, but merely that we have arrived at a proposition. 

The principle by which propositions of varying degrees of 
generality are manufactured from molecular propositions is as 
follows : 

Let <j> (ai, fZg, Og . • . Pj, Pg, P3 . . . Ri, Rg, R3 • . . ) be a molecular 

proposition which contains the proper names a^, ag, Og, ... the 
predicates Pi, Pg, P3 . . . the dyadic relations R^, Rg, R3 . . . and 
so on. All these are called the "constituents" of the proposition 
in question. Any one or more of these constituents may be re- 
placed by a variable, and the result asserted for some value or 
for all values of the variable. This gives us a large assemblage 
of general propositions all manufactured out of (not deduced 
from) the original molecular proposition. Take as a very simple 
instance, "Socrates is wise". This leads, by the above process, to 
the following ten propositions : 

Something is wise 
Everything is wise 




Socrates has some predicate 

Socrates has all predicates 

Something has some predicate 

Everything has some predicate 

There is some predicate that everything has 

Something has all predicates 

Every predicate belongs to something 

Everything has all predicates 

The process of substituting either some value or all values of 
a variable is called "generalization* '• It is not convenient to con- 
fine this term to the case of all values. 

The technical form of the principle of atomicity, as I said 
before, asserts that all propositions are either atomic, or mole- 
cular, or generalizations of molecular propositions ; or at least, 
that a language of which this is true, and into which any state- 
ment is translatable, can be constructed. This must be true if 
Wittgenstein*s principle of atomicity is true/The converse does 

not hold. As I shall explain in a mom<gHf, a less sweeping and 

more defensible form of the principle leads equally to the tech- 
nical form. It is in its technical form that the principle is important 

in logic. I think that Wittgenstein himself would now accept 
the modification in question, since I understand that he no longer 
believes in atomic propositions. As we saw in an earlier chapter, 
what is useful in logic is zxormc forms ^ and the modified principle 
allows them to be substituted for thfe original atomic propositions^ 
in which it was considered necessary that each word should stand 

fe , omening a«dm« of comply. 

The weakening of Wittgenstein's thesis, which makes it more 
plausible, is as follows. A name N may be in fact the name of 
a complex, but may not itself have any logical complexity, i.e, 
any parts that are symbols. This is the case with all names that 
actually occur. Caesar was complex, but "Caesar" is lo^cally 
simple, i.e. none of its parts are symbols. We might maintain 
that Wittgenstein's thesis is not to be applied to everything tbat 
is in fact complex, but only to things named by complex names, 



«C 9> 

E.g., though "Caesar" is simple, "the death of Caesar'' is com- 
plex. Instead of the phrase "every statement about complexes", 
which appears at the beginning of Wittgenstein's enunciation, we 
shall substitute: "every statement about complexes of which the 
complexity is made explicit in the statement". This meets the 
difficulty that would otherwise arise whenever we speak of some- 
thing which is in fact complex, but which we do not know to 
be so, or at any rate do not know how to analyse. 

Even in this weakened form, the principle forbids the occur- 
rence of /? as a unit in "A believes p'\ since a proposition must 
be explicitly complex, except in those unusual cases in which it 
has a proper name, such as the Pons Asinorvm ; and even then, 
we only arrive at what is asserted in "A believes />" when we 
substitute the proposition for its name. 

If either the thesis of extensionality or that of atomicity is to 
be maintained, it is necessary to distinguish between the 
in "A believes/?" and the "/?" in an ordinary truth-function such 
as "/> or q\ If the two are identical, it is impossible to construct 
a purely extensional logic,^ and it is probably impossible to main- 
tain physicalism in Carnap's sense. The attempt to distinguish 
between the two p's was first made by Wittgenstein (Tractatusy 
5.54 £). He says: 

"In the general propositional form, propositions occur in a 
proposition only as bases of the truth-operations. 

"At first sight it appears as if there were also a different way 
in which one proposition could occur in another. 

"Especially in certain propositional forms of psychology, like 

*A thinks, that/? is the case', or 'A thinks/?', etc. 

"Here it appears superficially as if the proposition /? stood to 
the object A in a kind of relation. 

"(And in modern epistemology (Russell, Moore, etc.) those 
propositions have been conceived in ^s way.) 

"But it is clear that *A believes that/?', *A thinks /?', *A says /?', 
are of the form * "/?" says/?': and here we have no co-ordination 

of a fact and an object, but a co-ordination of facts by means 
of a co-ordination of their objects. 





"This shows that there is no such thing as the soul— the 
subject, etc. — ^as it is conceived in contemporary superficial 

adopted Wittgenstein's view in the second edition 

Principia Mathematica (Vol, I, Appendix C), and so did Camap 
in Der logische Aufbau der Welu In The Logical Syntax 

Language* he makes a slight change : he says that intensional as 
well as extensional languages are possible, and that we must only 
say that every statement in an intensional language can be trans- 
lated into an extensional language. Even this he does not regard 
as certain, though he considers it plausible. On this question 
of propositional attitudes, however, he repeats what Wittgen- 
stein says. "Charles says (or thinks) A", he says, is, as it stands, 
intensional, but can be translated into "Charles says (or thinks) 
*A* *'. Here we are told: "let 'A' be an abbreviation (not a desig- 
nation) of some sentence". We are also told that syntactical 
designations are to be formed with inverted commas. All this 
adds nothing to what occurs in the Tractatus Logko-Philo- 

I have come to doubt whether this view, even if true, can be 

, ^TW* ** U*V^V., 

c< < 

maintained on Wittgenstein's grounds. I propose, therefore, to 
examine Wittgenstein's arguments controversially. 

The kernel of the passage just quoted from Wittgenstein is : 
A believes that p\ 'A thinks p\ *A says p% are of the form 
* "/>" says /?* ". Let us try to state this point of view clearly. 

In general, when a word occurs in a sentence, we are not 
speaking about the word, but about what it means; when we 
wish to speak about the word, we put it in inverted commas. 
Thus the sentence " 'Socrates' is the name of Socrates" is not 
a tautology; you learn a proposition of this sort when you are 
introduced to a person of whom you have never heard. When 
the word "Socrates" is not in inverted commas, you are speaking 
of the man, not the word. Now in like manner, when we assert 
a proposition, it is maintained that we are not saying anything 
about the words, but about what the words mean : and if we 


§ 67, p. 245 ff. 



want to say anything about the words, we must put them in 
inverted commas. But there is a difference between propositions 
and single words. Single words, at least such as are object- words, 
have a meaning which is external to language ; but propositions, 
since they can be false, must, except when they express percep- 
tions, have some less direct relation to objects. Thus the dis- 

between "/?" and p is not so simple as that between 
Socrates" and Socrates. 
The important distinction, in this discussion, is not between 


a M 

and /?, but between what p expresses and what it indicates. 
This distinction is not confined to propositions; it exists also in 
the case of object-words. If I exclaim "fire !" I express my own 
state and indicate an occurrence different from my state. The 
single word is a complete sentence. This is a prerogative of 
object-words; other words can only be parts of sentences, 
maintain that the use of an object-word as a complete exclamatory 
sentence is its primary use, from which its use as part of a larger 
sentence is derivative. It is qua sentence that an object-word has 
the two aspects of expression and indication. 

The distinction between ^significant and nonsensical strings of 
words compels us to recognize that a significant sentence has a 



non-linguistic property — ^namely "significance" 
nothing to do with truth or falsehood, being more subjective. 
We may identify the significance of a sentence with what it 
expresses, which is a state of the speaker. Such a state may be 

called a "believing", if the sentence is indicative. Two believings 
that can be expressed by the same sentence are said to be instances 
of the same "belief". 

From what has just been said, it follows that there are three 
ways, not two, in which a sentence may occur. 

First: we may be concerned with the actual words; 


; this 

the proper occasion for the use of inverted commas. For example, 
we may assert: Caesar said "jacta est alea". A person who knows 
no Latin can know that Caesar said this; it is not necessary that 
he should know what Caesar meant. Therefore the words "jacta 
est alea" occur here as words, not as having meaning. 



Second: we may be concerned with what the sentence ex- 
presses, and be indifferent as to what it indicates; this happens 
if we assert : Caesar said that the die was cast. Here the words 
"the die was cast" occur as having significance; Caesar did not 
use these words, but Latin words expressing the same state. If 
we asserted: Caesar said "the die is cast", our assertion would be 
false, since it would imply that he spoke English. Thus when 
we say: "Caesar said that the die was cast", the significance of 
the words "the die was cast" is relevant, but not the indication, 
since it is entirely irrelevant whether, in fact, the die was cast 

or not. 

Third: we may be concerned, not only with what a sentence 
expresses, but also with what it indicates. I may say: "The die 
was cast, as Caesar truly said". Here, when I say "the die was 
cast", I make an assertion, which is true if the sentence indi- 
cates something, and false if it indicates nothing. In every com- 
plete sentence in the indicative, the indication is relevant, but in 
subordinate sentences it may happen that only what is expressed 
is relevant. This happens, in particular, as regards the p in "A 

believes p\ 

We can now decide what we are to think of Wittgenstein's 
view that "A believes/?" is of the form: " y says/*. Or rather, 
we can decide whether we should say "A believes p" or 
believes p' ". Let us put for "/?" the sentence "B is hot". When 

we say that A believes that B is hot, we are saying (roughly) 
that A is in a state which will lead him, if he speaks, to say 

"B is hot" or something having the same significance. We are 
not saying that these words are in A's mind ; he may be a French- 
man who, if he spoke, would say "B a chaud". We are, in fact, 
saying nothing about the words "B is hot", but only about what 
they signify. Therefore there should be no inverted commas, 
and we should say: "A believes /' . 

Should we say "/? is true" or " /?' is true".'^ 

It is generally assumed that we should say the latter, but I 

think this assumption is wrong. 
Consider "it is true that B is hot". 



This asserts a complicated relation between a class of believings 
and an event. It means : any person who is in one of a certain 

class of states [to wit, those expressed by the words "B is hot"] has 

wit, B's being hot, or 


a certain relation to a certain event 
not-hot, as the case may be]. 

Here the words "B is hot" enter only through the significance 
of the phrase, not as words. Therefore we should say: 




The difficulty of the subject, I repeat, . arises from the fact that 
sentences, and some words, have two non-verbal uses, (a) as 
indicating objects (h) as expressing states of mind. Words may 


through their significance, and not as words, without 


occurring as indicating: this happens when they occur as only 
expressing. Single words other than object-words only express 
and do not indicate. That is why, unlike object-words, they can- 
not be complete sentences. 

The above makes it clear that * y ' may occur in two different 
non-verbal ways, (a) where both indication and expression are 
relevant, and (b) where only expression is relevant. When the 
sentence occurs by itself; as an assertion, we have (a) ; when we 

believes p", we have (^), since the occurrence we are 

say •' 

asserting can. be completely described without reference to the 
truth or falsehood of /?. But when 

we assert "/? or q" or any 

other truth-function, we have (a). 
The principle of extensionality, if the above analysis is correct 


applies to all occurrences of *y * in which its indication is rele 
vant, but not to those in which only the expression is relevant 
i.e. it applies to (a), not (i). This statement, I think, is a tautology. 
The principle of extensionality in its general form must, if I am 
not mistaken, be rejected. 

has been suggested to me 

believes that B is hot", the words 

Mr. N. Dalkey that in " 

that B is hot" descrihe what 

is expressed by **B is hot" when this is a complete sentence. This 
view is attractive, and may be right. According to this view, the 
words "that B is hot" do not really refer to B, but describe A*s 
state. The case is analogous to that in which 





a smell of roses**. Here roses only come in as describing A's 
state; I might give a name, say S, to the smell, and say "A smells 

. Similarly I might (in theory) substitute for "that B is hot** 
words descriptive of the state of mind and body existing in those 

who are engaged in believing that B is hot. This view makes 

it necessary to draw a sharp distinction between 'y and "that 


Whenever it is really "/>" that occurs, we can preserve the prin 
dple of extensionali ty ; but when it is "^^ " '^ 


that occurs 

reason for the failure of the principle is that "/>" is not, in fact, 

We have now to consider the principle of atomicity. I shall 
not now consider it generally, but only in relation to such sen- 
tences as "A believes p\ In its general form it requires a con- 
sideration of analysis, and of the question whether proper names 
for complexes are theoretically indispensable, which I propose 
to leave to a later stage. For the present I wish only to consider 

whether such sentences as "A believes 


can, in a suitable 

language, be expressed within the hierarchy of atomic, molecular, 

and generalized sentences explained earlier in this chapter. 

The question is: can we interpret /*A believes p 
does not appear as a subordinate complex } 



For ''p 


let us again take "B is hot". We agreed in an earlier 

chapter that to say A believes this is to say that he is in one of 
a number of describable states, all which have something in 

common. One of such states is that in which A exclaims 



hot!", but there is no reason to suppose that any words are 
necessarily present to A when he is believing that B is hot. 

To say "A exclaims *B is hot!' " is to assert a series of move- 
ments in A's speech-organs j this is a purely physical occurrence, 
which CcPi be completely described without introducing any 

subordinate complex. It would seem that every other state of 
A which is a believing that B is hot could be similarly described. 
The question remains, however: what do all these states have 

m common 


I think that what they have in common is only causal This, 
however, is a difficult question, and one which, I believe, it is 



not necessary 


to answer with any precision 

seems to 

me that no answer which is at all likely to be correct can interfere 
with the conclusion that "A believes /?" can be analysed without 

introducing a subordinate complex p^ at any rate 


simple sentence such as 



IS a 


is a general sentence 


such as "all men are mortal", the matter is more difHcult. I shall 

therefore, for the 

moment, content myself with the provisional 

conclusion that, so far, we have found no good argument against 
the principle of atomicity. 

We thus reach the conclusions (i) that the principle of exten- 
sionality is not shown to be false, when strictly interpreted, by 
the analysis of such sentences as "A believes /?"; (2) that this 
same analysis does not prove the principle of atomicity to be 
false, but does not suffice to prove it true. 


H J 


Chapter XX 


In general, in this book, I am avoiding logical questions, but in 

this chapter, as in the last, I shall be concerned with a logical 
topic, namely the law of excluded middle. As every one knows, 
Brouwer has challenged the law, and has done so on epistemo- 
logical grounds. He, in common with many others, holds that 
"truth" can only be defined in terms of "verifiability", which is 
obviously a concept belonging to theory of knowledge. If he is 
right, it follows that the law of excluded middle, and the law of 
contradiction also, belong to epistemology, and must be recon- 
sidered in the light of whatever definition of truth and falsehood 
epistemology permits. We considered truth and falsehood in a 
preliminary manner in Chapter XVI,^a'hd discussed the attempt 
to define them epistemologically. It is fairly obvious that, if an 
epistemological definition is adhered to, the law of excluded 
middle, in its usual form, cannot be true, though the law 
contradiction may be. We have to consider, in this chapter and 
the next, whether to sacrifice the law of excluded middle or to 
attempt a definition of truth which is independent of knowledge. 
The difficulties of either view are appalling. If we define tmth 
in relation to knowledge, logic collapses, and much hitherto 
accepted reasoning, including large parts of mathematics, must 
be rejected as invalid. But if we adhere to the law of excluded 
middle, we shall find ourselves committed to a realist metaphysic 
which may seem, in the spirit if not in the letter, incompatible 
with empiricism. The question is fundamental, and of the greatest 

* What is said in this chapter is intended to clarify the question. It is only in 
the next chapter that a serious attempt is made to reach a decision. 




Before attempting to decide it, let us develop the alternatives. 

Brouwer is not concerned with phrases that are syntactically 
nonsensical, such as "quadruplicity drinks procrastination". He 
is concerned with sentences that are grammatically and logically 
correct, but episteniologically incapable of being proved or dis- 
proved. We must be clear as to the point at issue before we 
begin to discuss it. 

Brouwer argues that "true*' is a useless conception unless we 
have ways of discovering whether a proposition is true or not. 

He therefore substitutes "verifiable" 



call a proposition 




and he does not 


unless its contradictory is verifiable. 

There thus remains an intermediate class of propositions, which 
are syntactically correct, but neither verifiable nor the con- 
tradictories of verifiable propositions. This intermediate class 
Brouwer refuses to call either true or false, and in regard to them 
he regards the law of excluded middle as mistaken. 
No one has yet gone so far as to define 




truth" is " 




known"; the epistemological definition of 
be known". The word "verifiable" is commonly used, and a 
proposition is verifiable if it can be verified. This at once intro- 
duces difiiculties, since possibility is an awkward concept. If the 
definition is to be definite, the particular kind of possibility that 
is intended will have to be elucidated. In mathematics, Brouwer 
and his school have done this, with a considerable measure of 
success; but so far as I know, they have given little thought to 
more ordinary propositions, such as historical hypotheses con 
ceming which there is no evidence either way. Much is to be 
learnt from Camap's Logical Syntax ofLanguage^ but mainly by 
way of suggestion. He holds that a general proposition, such 
as "all men are mortal", which is inherently incapable of 
being completely proved, is to be taken (provisionally) as true 
many instances of its truth are known, and none of its 

definition of 




what can be known" will have 

to advance step by step from basic propositions. I shall assume, 
in accordance with what was said in Chapter XI, that my present 





factual premisses consist of: (i) a very small number asserting 
present percepts; (2) a considerably larger number of negative 
propositions derived from present percepts as we arrive at "this 
is not red" when we see a buttercup; (3) memories, in so far 
as no argument exists to throw doubt on them ; (4) the law of 
contradiction, but not the law of excluded middle. The law 
excluded middle will be true, to begin with, of a certain class 
of propositions, namely those that can be confronted with per- 
cepts. If you are letting off fireworks on the fifth of November, 
and you say "look out, there's going to be a bang", either there 
is a bang, or the fireworks are damp and there isn't. In such a 
case, your statement is true or false. There are other cases, derived 
from this kind, to which the law of excluded middle applies ; the 
definition of the class of cases is much the same problem as the 
epistemological definition of "truth". 

is to be observed that, when the law of excluded middle 
fails, the law of double negation also fails. If p is neither true 

nor false, it is false that p is false; if the principle of double 
negation held, this would imply that p is true, whereas. 

hypothesis, p is neither true nor false. "Consequently, in this 

logic, "it is false that p is false" is not equivalent to "/? is 

true' ' 

To give ourselves a chance, we will, at least to begin with, 
allow inductive generalizations from basic propositions. These 
may turn out to be false if a negative instance occurs; until that 
happens, we shall, following Carnap, provisionally accept them 
as true. In either case, we shall regard them as subject to the 
law of excluded middle. We will allow also the testimony of 
others, subject to common sense provisos. We can now build 
up science; and having accepted inductive generalizations, we 
will admit as true such of their consequences as cannot be dis- 
proved. For example, we will say that eclipses occurred in pre- 
historic times as astronomy leads us to suppose; but we say this 
with the degree of hesitation appropriate to the inductive gene- 
ralizations that constitute the laws of astronomy. 

We can thus assert and deny all propositions that, as empiri- 


I * 




cists, we see reason to assert or deny. The difficulties come (a) in 
logic and mathematics (b) as to extra-logical propositions in 
regard to which there is no evidence either way 

Let us consider a definite extra-logical proposition as to which 



no evidence. Take "it snowed on Manhattan Island on 

the first of January in the year i a.d'*. Let us call this proposi- 

What do we know about P ? Having accepted inductive 




generalizations, history tells us that there was a year i a.d 
and geology assures us that Manhattan Island existed then. We 
know that snow often falls there in winter. We therefore under- 
stand P just as well as if it related to a snowfall of which there 
is historical record. In theory, a Laplacean calculator could infer 
the weather of former times, just as the astronomer infers the 
eclipses. In practice, however, this is impossible, not only because 
the calculations would be too difficult, but because more data 
would be required than could ever be obtained. We must there- 
fore admit that we have not any evidence as to whether 

far as 


true or false, and that,- so far as we can see, we are never likely 

to have any 

We must conclude, if 




is to be defined 

epistemologically, that P is neither true nor false. 

Our reluctance to accept this conclusion comes from our 
obstinate belief in a "real" world independent of our observa- 
tion. We feel that we might have been there, and we should then 
have seen whether it was snowing, and the fact of our looking 
on would have made no difference to the snow. We are ready 

enough to concede that the whiteness of the snow*s appearance 
has to do with our eyes, just as the cold feeling has to do witli 
our temperature nerves ; but we suppose these sensations to have 
an outside cause, which is the snow as dealt with in physics. 
And this, we believe, except where certain very delicate quantum 
observations are concerned, is just the same whether we know 
of it or not. 

But all this was already conceded when we accepted inductive 
generalizations, and allowed ourselves to believe that Manhattan 
Island probably existed at the date in question. If we are going 
to allow inductions of this sort, there seems no reason for re- 


I. •• 


fusing to extend the law of excluded middle to every proposition 
for or against which there is any evidence, however slender. 
Now there might easily be evidence that the climate of Manhattan 
Island has not changed much in the last two thousand years, and 
in that case weather records give the probability of snow on 
any given day of the year. We shall therefore conclude that P 
is either true or false, for, though we cannot decide the question, 
we know something of the likelihood of each alternative. 

There will still be propositions as to which there is no evidence 
whatever, for instance: "there is a cosmos which has no spatio- 
temporal relation to the one in which we live". Such a cosmos 
can be imagined by a writer of scientific romances, but by the 
very nature of the hypothesis there can be no inductive argument 
either for or against it. When we feel that there must be or not 
be such a cosmos, I think that we imagine a Deity contemplating 
all the worlds that He has made, and thereby we surreptitiously 
restore the link with our own world which, in words, we have 

, «* „^-.«w, 

denied.* If we rigidly exclude both this conception and that of 
a miraculous heightening of our own perceptive faculties, it is 
perhaps possible to suppose that our hypothesis has no meaning. 
In that case, it is neither true nor false, but it is not a proposition, 
and therefore fails to show that there are propositions which do 
not obey the law of excluded middle. 

We must face the question: in what circumstances, if any, 
does a sentence which is syntactically correct fail to have a 
meaning? We suggested, a moment ago, that perhaps the sen- 
tence: "something has no spatio-temporal relation to my present 
percept", is devoid of meaning; for that is what the rejection 
of the imagined cosmos amounts to. It seems to follow that the 
contradictory of the above sentence, namely: "everything has 
some spatio-temporal relation to my present percept", is also 
devoid of meaning; but this seems far less plausible. If this is 
to be meaningless, it must be because of the word "everything 
The word "everything", it may be said, implies that the whole 
universe can be laid out for inspection, whereas, in fact, new 

* Cf. The Star Maker^ by Olaf Stapledon. 




Dercepts perpetually occur, and all totality is illusory except that 
:>{ an enumerated set of objects* 

This question of totality is very important. Can we define 
* total conceptually, as we define the class of men or the class 
3f natural numbers ? Some think that we can do so if the class 
's finite, but not otherwise, I cannot see, however, that this is 

, "^"V-Tl-i., 

1 relevant consideration, except when a general word is a mere 
abbreviation for "these objects in this given collection". In that 
:ase, the general word is unnecessary. Whenever, as in the case 
of men, actual enumeration is impossible, the question whether 
the collection is finite or infinite seems irrelevant. "All men are 
mortal" raises the same problems, in this connection, as "all 
integers are odd or even". 

When we say "all men are mortal", are we saying anything, 
or are we making meaningless noises .'^ I am not asking whether 
the sentence is true, but whether it is significant. Let us first 
exclude some untenable views, (i) We cannot try to reduce the 
proposition to a prescription, to wit : "if I see a man> I shall 
judge him to be mortal". For the occasions on which I shall see 
a man are just as impossible to enumerate as men are. I might, 
with my dying breath, say "all the men I have met were mortal", 
because then they could be enumerated; but until then the col- 
lection is only defined conceptually. (2) We cannot say : "a state- 
ment about a collection is legitimate when there is a possible set 
of experiences which would cover the ^ whole collection, but not 
otherwise". For we shall find, if we attempt to define "possible 
experiences", that we are taken into just the hypothetical con- 
ceptual realm from which we wished to escape. How are we to 
know whether an experience is "possible" ? Obviously this will 
require knowledge that transcends actual experience. (3) We 
cannot confine "all men are mortal" to past experience, for in 
that case it would have to mean "all the men who have died 
hitherto were mortal", which is a tautology. (4) It is sometimes 
thought possible to interpret general statements — especially in- 
ductive generalizations — ^as practical advice. Thus "all men are 
mortal" will mean: "next time you meet a man, I should advise 



you to behave as if he were mortal, for if you chop his head in 
two in the hope that he is immortal, you will be hanged". But 

this advice is only sound because the man is mortal. If you 
seriously doubt whether all men are mortal, you may do well 
to go about making experiments on the subject. The pragmatic 
interpretation, in fact, is only an evasion. 

If we exclude such sentences as "all men are mortal'*, which 
deal with collections defined conceptually, general propositions 
will be confined to history, or rather to collections composed of 
objects which now exist or have existed. "We can say "all the 
men in this room will die", but not "all the children of the men 
in this room will die". This is surelv absurd. 

seems to me that, when we understand the words 
and "mortal", we can understand "all men are mortal", without 
having to be acquainted with each individual man. And in like 
manner, I should say, we can understand "all integers are odd or 

'. But if this view is to be maintained, there must be such 




a thing as understanding "all-ness", independently of enume 
ration. This is really a question of understanding what is hypo 
thetical. The analysis of general propositions is very difficult 
since it seems quite clear that we can know propositions about 
all of a collection without knowing its several members. We say 
that "I hear nothing" may be a basic proposition; yet it is for 
logic a statement about everything in the universe. We have 
seen in Chapter XVIII how to avoid this difficulty. 

When we were discussing snow in i A.D., we allowed our- 

in realist terms, i.e. 

selves to accept inductive generalizations. It is questionable 
whether, when we are doubting the law of excluded middle, we 
have any right to do this, except at most in the way of inferring 
percepts. Inductions in the physical sciences are always phrased 

, they suppose that what you observe can 
happen without your observation, and does happen in suitable 
circumstances. If we arrive at an uninhabited island and find 
luxuriant vegetation, we shall infer that it has rained there, 
although no one has seen the rain. Now it is obvious that, from 
the standpoint of inductive verification, two hypotheses which 





nly differ as to unobserved occurrences are precisely on a level, 
'rem the epistemological point of view, therefore, we may 
ippose that there are no unobserved occurrences, or that there 
lea few, or that there are many; we can, as physicists do, insert 
/hatever number and kind of unobserved occurrences will make 
: easiest to formulate the laws of observed occurrences. They 
erve the same sort of purpose as may be served by complex 
lumbers in a calculation which begins and ends with real 

Is there any sense in asking whether these unobserved occur- 
-ences really occur? According to Carnap, there is only a lin- 
Tuistic question: "reality** is a metaphysical term for which there 
"s no legitimate use. Well and good, but let us be consistent. 

have not myself observed what I have learnt from testimony 


or from history; I have observed only what has come within 
my own experience. Therefore, on the view in question, the 
hypotheses that testimony is not merely noises or shapes, and 
that the world existed before the earliest moment that 
remember, are mere linguistic conveniences. 


This view is one whieh, in fact, no one accepts. If a doctor 
says to you "your wife has cancer", you feel no doubt that what 
you hear expresses a thought; you also have no doubt that. 

the doctor is right,. your wife is having and will have painful 
experiences which will not be yours. Your emotions would be 
quite different if you thought the whole thing merely a linguistic 
abbreviation for describing certain experiences of your own. This, 
of course, is no argument. But I notice that those who take the 
sort of view that I am combating always avoid apjplying it as 
against other human beings, and are content to apply it to such 
matters as the glacial epoch, which have very little emotional 
content. This is illogical. If the glacial epoch is only a linguistic 
convenience, sp are your parents and your children, your friends 


your colleagues. It is, of course, still possible to 



testimony. You may say: "Mr. A, so far as I know, is a series 
of noises and shapes; but I have found, odd as it may seem, that 
if I interpret the noises as those which I should make to express 




certain thoughts or percepts, they frequently turn out to be true. 
I have therefore decided to behave as if Mn A were an intelligent 
being'*. But your emotions will not be what they would be if 
you believed that he "really" had intelligence. 

When we ask: "do any occurrences not observed by me really 
occur ?" we are asking a question which, at least as regards odier 
human beings, has a very great emotional content, and can hardly, 
it would seem, be totally devoid of significance. We are interested 
in other people's loves and hates, pleasures and pains, because 
we are firmly persuaded that they are as "real" as our own. We 
mean something when we say this. A person in a novel manifests 
himself, but deceptively: the emotions which he expresses have 
not been actually felt. "Real" people are different; but how? 

I am not concerned, at the moment, to argue that unobserved 

events occur; I am only concerned to argue that the question 
whether they occur or not is more than a linguistic question, 
take the question, to begin with, in connection with the per- 
cepts, thoughts, and feelings of other people, because in that case 
what we are inferring is closely analogous to what we know 
from our own experience. In the case of unobserved matter, there 
is not only the fact that it is unobserved, but that it must be 
very dijfferent from anything of which we have experience, since 
it cannot have any sensible qualities. This additional problem 
is avoided by considering the experiences of other people. If we 
see a man apparently suffering, the hypothesis that he is suffering 
adds something, and is not merely the adoption of a different 

linguistic convention from that of the solipsist. 

It is no use to say: "but this does not take you outside expe- 
rience; it only takes you outside your experience". You do not 
know that this is true unless you know that the other man has 
experiences, and is not merely what you perceive; but this is 
the very piece of knowledge that was to be justified. Epistemology 
cannot iegin by accepting testimony, for the correctness of testi- 
mony is certainly not among basic propositions. 

I conclude, then, that there is a substantial meaning in the 
hypothesis that something occurs which I do not experience, at 



least when this is something analogous to my experiences^ e.g. 
the experiences which I attribute to other people. 

This, however, does not settle the question whether there is 
any meaning in the hypothesis of physical phenomena which 
are observed by no one, which we must now consider. 

There are here certain distinctions to be made. On empirical 
grounds we believe that there cannot be visual objects except 
where there are eyes and nerves and a brain, but there is no 
logical difficulty in the hypothesis of such objects existing else- 
where. In fact, every person who is philosophically and scien- 
tifically naive believes that what we see when we look at some- 
thing is still there when we are no longer looking. This is what 
is called naive realism — ^a doctrine which must be held to be false 
in fact, but not logically impossible. The problem in connection 
with physics is : having admitted that where there is no sentient 
percipient there cannot be anything having the sensible qualities 
that we know from experience, is 


any meanmg m 



hypothesis that there is something there ,'* There are in fact two 
questions : First, is there significance in the hypothesis that some- 
ihing not experienced exists } Second, is there significance in the 
hypothesis that something exists which is as unlike objects of per- 
ception as we should have to suppose occurrences to be where 

there are no percipients : 

As to the first, I see no difficulty. The fact that we experience 
a phenomenon is not an essential part of our understanding of 
the phenomenon, but only a cause of our knowledge that it 
occurs, and there is no logical obstacle to the hypothesis that the 
phenomenon could exist unperceived. In fact, we all hold that 
we have many sensations which we do not notice, and these are, 
strictly speaking, not experienced. 

There is more difficulty as to the second question, namely: 
is there any significance in the hypothesis of physical phenomena 
as different from our percepts as they would have to be if they 
were neither visual nor auditory nor of any of the familiar kinds .^ 
The question is not quite that of the Kantian Ding-an-Sich^ which 
is outside time; the kind of occurrences concerning which we 



are inquiring are certainly in time, and they are in space of a 
sort, though not quite of the sort to which we are accustomed 
in percepts. Physical space — ^i.e. the space of physics — is not 
directly sensible, but is definable by relation to sensible spaces. 
It would seem, dierefore, that a proposition concerning a purely 
physical phenomenon can be enunciated in terms which are known 
through experience; if so, the proposition is certainly, in one 
sense, significant, even if we do not know how to discover 

whether it is true or false. If it is significant to say "everything 
that exists is sensible", the contradictory of this, namely "some- 
thing non-sensible exists", must also be significant. If it be main- 
tained that "sensible" has no meaning, we can substitute "visual 

or auditory, or etc." It seems, therefore, that we cannot deny 
significance to the hypothesis of occurrences having none of the 
qualities which we believe to be causally dependent upon a sen- 


It remains to inquire in what sense, if any, such a hypothesis 
can be regarded as either true or false. 

This brings us to the question of "fact" as what makes pro- 
positions true. According to the correspondence theory of truth 
as Tarski points out, the proposition "it is snowing" is true if 
it is snowing. This hzs, prima facie^ nothing to do with knowledge. 
If you do not realize that it is snowing, that does not make 


less true. You may find 
several inches of snow on the ground when at last you do 

proposition "it is snowing" any 

look out, and say "it must have been snowing for hours". Surely 
it would have been snowing just the same if you had not been 
going to look out afterwards.'^ All the time diat you were not 
looking out, the proposition "it is snowing" was true, although 
you did not know that it was. This is the view of realism and 
of common sense. And it is this view which has made the law 
of excluded middle seem self-evident. 

Let us set to work to state this view in such a way as to avoid 
all avoidable difficulties. First, as to "facts" : they are not to be 
conceived as "that grass is green" or "that all men are mortal 
they are to be conceived as occurrences. We shall say that 



percepts are facts, but according to the realist view they are only 
some among facts. They may be defined as facts that some one 
knows without inference; but on the realist hypothesis there are 
other facts which can only be known by inference, and perhaps 
yet others which cannot be known at all 

Percepts, in this view, may be defined as events having a 
certain kind of spatio-temporal relation to a living body with 
suitable organs. Suppose, for example, you are measuring the 
velocity of sound, and for this purpose you occasionally fire a 
gun, while a man a mile away waves a flag as soon as he hears 
the ri 

believe the physicists — there are events, namely air-waves. When 
this train of events reaches an ear, it undergoes various modi- 
fications, much as sunlight undergoes modifications when it sets 
up the manufacture of chlorophyll in plants. One of the events 
resulting from the impact of sound-waves on an ear, provided 
the ear is attached to a normal brain, is what is called "hearing"* 
the sound. After this event, the chain of causation runs out of 
the brain into the arm, and leads to the waving of the flag. What 
is odd about the brain ^nd the sensation is the character of the 
causal laws that operate at this point in the chain: they involve 

port. Throughout the intervening 

we are to 

habit, and 

"mnemic" causation 

To say that we "know" 


cept is to say that it has set up a certain habit in the brain. Only 
events in the brain can set up habits in the brain ; therefore only 
events in the brain can be known in the kind of way in which 
we know percepts. 

Some such view as the above is assumed technically in physics 
and physiology. I do not mean that physicists and physiologists 
are necessarily prepared to defend it theoretically, or that their 
results are not compatible with other views. I mean only that the 
language they naturally use is one which implies some such 

I do not know whether there is any argument which shows 
that this view is false. Various idealistic philosophies have 
attempted to prove it untenable, but in so far as they appealed 
to logic I shall take it for granted that they failed. The argument 




from epistemology, which unlike that from logic, is as powerful 
as it ever was, does not attempt to show that the view in 
question is false, but only that it is gratuitous, in the sense that 
it sins against Occam's razor by assuming the existence of un- 
necessary entities. What we know, says the epistemological 
argument, is percepts; the sound-waves, the brain, etc, are mere 
convenient hypotheses in the interconnecting of percepts. They 
enable me, when I have fired my shot, to calculate how long 

(according to the visual perceptions which I call "seeing a stop 

watch*') it will be before I have the percept which I call the 

waving of the flag. But there is no more need to suppose that 
these hypotheses have any "reality" than there is to suppose that 
parallel lines "really" meet in a point at infinity, which also is 
for some purposes a convenient way of speaking. 

This epistemological scepticism has a logical foundation, 
namely the principle that it is never possible to deduce the 
existence of something from the existence of something else. This 
principle must be stated more clearly, and without the use of 
the word "existence". Let is take an illustration. You look out 
of the window, and observe that you can see three houses. You 
turn back into the room and say "three houses are visible from 

the window". The kind of sceptic that I have in mind would 
say "you mean three houses were visible". You would reply "but 
they can't have vanished in this little moment". You might look 
again and say "y^^> there they are still". The sceptic would 

retort: "I grant that when you looked again they were there 
again, but what makes you think they had been there in the 

interval.'^" You would only be able to say "because I see them 
whenever I look". The sceptic would say "then you ought to 
infer that they are caused by your looking". You will never 
succeed in getting any evidence against this view, because you 
can't find out what the houses look like when no one is looking 
at them. 

Our logical principle may be stated as follows : "no proposi- 
tion about what occurs in one part of space-time logically implies 
any proposition about what occurs in another part of space-time". 




If the reference to space-time is thought unduly suggestive of 
physicalism, it can easily be eliminated. We may say: "the 
perceptive propositions derivable from one perceived event never 
logically imply any proposition about any other event". I do not 
think this can be questioned by any one who understands the 
logic of truth-functions. 

But outside pure mathematics the important kinds of inference 
are not logical ; they are analogical and inductive. Now the kind 
of partial sceptic whom we have been having in mind allows 
such inferences, for he accepts physicalism whenever it enables 
us to prophesy our own future percepts. He will allow the man 
measuring the velocity of sound to say "in five seconds I shall 
see the flag wave"; he will only not allow him to say "in five 
seconds the flag will wave". These two inferences, however, 
are exactly on a level as regards induction and analogy, without 
which science, however interpreted, becomes impossible. Our 
logical foundation thus becomes irrelevant, and we have to con- 
sider whether induction and analogy can ever make it probable 
that there are unperceived events. 

At this point there is' danger of a fallacy, so simple that it 
ought to be easy to avoid, but nevertheless not always avoided. 

man may say: "everything that I have ever perceived was 
perceived ; therefore there is inductive evidence that everything is 
perceived". The argument would be the same if I said: "every- 
thing I know is known; therefore probably everything is known" 

We are left, then, with a substantial question: assuming the 
legitimacy of induction and analogy, do they afford evidence 
for unperceived events.^ This is a diificult but by no means 

insoluble question. I shall, however, not discuss it now, since 
it assumes as conceded, what is for us at present the essential 
point, that the difference between a theory which allows unper- 
ceived events and one which does not is a difference which need 

not be merely linguistic. 
Although the above discussion has been so far very incon- 

clusive, I find myself believing, at the end of it, that truth and 
knowledge are different, and that a proposition may be true 


I I 










although no method exists of discovering that it is so. In that 
case, we may accept the law of excluded middle. We shall define 

(I am speaking of non-logical 


"truth" by reference to "events" 

truth), and "knowledge" by relation to "percepts". Thus "truth" 
will be a wider conception than "knowledge 



practically useless conception, but for the fact that knowledge has 
very vague boundaries. When we embark upon an investigatioiL 
we assume that the propositions concerning which we are in- 
quiring are either true or false; 

we may find evidence, or we 



as well as "knowledge", because the boundaries 

may not. Before the spectroscope, it would have seemed impos- 
sible ever to ascertain the chemical constitution of the stars ; but 
it would have been a mistake to maintain that they neither do 
nor do not contain the elements we know. At present, we do 
not know whether there is life elsewhere in the universe, but we 
are right to feel sure that there either is or is not. Thus we need 

knowledge are uncertain, and because, without the law of ex- 
cluded middle, we could not ask the questions that give rise 
to discoveries. 

In the following chapter, I shall continue the discussion 
the questions we have just been considering, but the discussion 
will be intensive and analytical rather than discursive. Before 
proceeding to minute analysis, I wished to make clear the bearing 
of the question at issue upon matters of general interest. This 
course involves some unavoidable repetition, which I must ask 
the reader to excuse. 

> 1 













H •, 

Chapter XXI 


In recent philosophy we may distinguish four main types of 
theory as to "truth'* or as to its replacement by some concept 
which is thought preferable. These four theories are : 

, The theory which substitutes "warranted assertibility" for 
"truth". This theory is advocated by Dr. Dewey and his school. 
IL The theory which substitutes "probability" for "truth". 
This theory is advocated by Professor Reichenbach. 

III. The theory which defines ' "truth" as "coherence". This 
theory is advocated by Hegelians and certain logical positivists. 

IV. The correspondence theory of truth, according to which 
the truth of basic propositions depends upon their relation to 
some occurrence, and the truth of other propositions depends 
upon their syntactical relations to basic propositions. 

For my part, I adhere firmly to this last theory. It has, however, 
two forms, between which the decision is not easy. In one form, 
the basic propositions must be derived from experience, and 
therefore propositions which cannot be suitably related to 
experience are neither true nor false. In the other form, the basic 
propositions need not be related to experience, but only to "fact", 
though if they are not related to experience they cannot be known. 

Thus the two forms of the correspondience yt^Q^ry^.d^^^^ ^ ^^ 
the relation of "truth" to "knowledge". 

Of the above four theories, I have discussed the third in 
Chapter Xj the first and second, which have a certain affinity, 
I shall discuss in a later chapter. For the present, I shall assume 
that "truth" is to be defined by correspondence, and examine 
the two forms of this theory, according as "experience" or "fact 


is taken as that with which truth must correspond. I will call 





these two theories the '^epistemological" and the "logical" theory 
respectively. I do not mean to suggest that the "logical" theory 
is more logical than the other, but only that it is the one tech- 
nically assumed in logic, which is involved in certain difficulties 
if the theory is rejected. 

Over a great part of the field, the two theories are identical. 
Everything that is true according to the epistemological theory 
is also true according to the logical theory, though not vice versa 
All the basic propositions of the epistemological theory are also 
basic in the logical theory, though again not vice versa. The 
syntactical relations of basic propositions to other true. pro- 
positions are the same in both theories. The propositions diat 
can be known empirically are the same in both theories. There 
are differences, however, in regard to logic ; in the logical theory 
all propositions are either true or false, whereas in the epistemo- 
logical theory a proposition is neither true nor false if there is no 
evidence either for or against it. That is to say, the law of ex- 
cluded middle is true in the logical theory, but not in the episte 
mological theory. This is the most important difference between 

will be observed that the correspondence used in defining 
"truth", in both theories, is only to be found in the case of basic 
propositions. Such a proposition as "all" men are mortal". 

assuming it true, derives its truth from "A is mortal", "B is 
mortal", etc., and each of these derives its truth from such pro- 
positions as "A grows cold", "B grows cold", etc. These pro- 

positions, for certain values of A and B, can be derived from 
observation; they are then basic propositions in both theories. 
They will (if true) be basic propositions in the logical theory, 
even when they are not observed; the logical theory will hold 
that there is a "fact" which would make the statement "A grows 
cold" true, even if no one is. aware of this fact — or, alternatively, 
that there is an opposite fact, or rather set of facts, from which it 
would follow that A is immortal. 

In the epistemological theory, basic propositions are defined 
as in Chapter X. In the logical theory, they must have a definition 


fc ft 


not referring to our knowledge, but such that, with this new 
logical definition, "experienced basic propositions'* become 
identical with "basic propositions" in the epistemological theory. 
The logical definition is to be obtained by observing the logical 
form of epistemologically basic propositions, and omitting the 
condition that they must be experienced, while retaining the 
condition that they must be true (in the sense of the logical 


In the epistemological theory, we say that a "basic" sentence 
is one that "corresponds" to an "experience", or "expresses" an 
"experience". The definition of "corresponding" or "expressing" 
is in the main behaviouristic. "Experience" can be surveyed, but 
on our present view it can hardly be defined. On the alternative 
"logical" view, "experiences" can be defined as a certain sub-class 

of "facts". 

Sentences which express experiences are of certain logical forms. 
"When they express such experiences as supply the data of physics, 
they are always atomic. As regards the data of psychology, there 
are difficulties in maintaining that this is the case, but we have 
seen reason to think these ^difficulties not insuperable. There are 
recollections involving logical words such as "or" and "some"; 
more generally, there are "propositional attitudes", such as 
believing, doubting, desiring, etc. The question of propositional 
attitudes is complex, and involves considerable discussion, but 
our analysis of belief has been intended to show that the basic 
propositions in regard to them are not essentially different from 

those required in physics. 

Assuming the logical forms of epistemologically basic sen- 
tences decided, we can proceed to consider the logical theory of 
basic sentences. But it must be said that the point of view we are 
now to consider is disputable. Its main merit is that it allows us 
to believe in tlie law of excluded middle. 

If the law of excluded middle is assumed, any sentence which 
is epistemologically basic will remain true-or-false if any word 
in it is replaced by another word of the same logical type. But 
when a sentence is epistemologically basic, the fact to which it 



corresponds, and in virtue of which it is true, is experienced. 
When one or more of the words in the sentence are changed, there 

may be no experience which is expressed by the new sentence- 
there may also be no syntactical relation to any epistemologically 
basic sentence in virtue of which the new sentence has derivative 
truth or falsehood. Therefore we must either abandon the law 
of excluded middle or enlarge our definition of truth. 

If, reverting to the epistemological theory, we abandon the 
law of excluded middle, we can define derivative truth in terms 
of **verifiability" : a sentence is "verifiable" when it has one of 
certain assigned syntactical relations to one or more epistemo- 

logically basic sentences. A sentence which has no such syn- 
tactical relation will be neither true nor false. (Certain syntactical 
relations to basic sentences make a sentence "probable"; in this 
case, also, we shall be obliged, on our present plan, to deny that 
the sentence is true-or-false.) 

Per contra^ we may adhere to the law of excluded middle, and 
seek a logical as opposed to an epistemological definition 

"basic sentences". This course requires, first, a definition of 
"significant" sentences. For this purppse we set up the following 

definitions : 

A sentence is "verifiable" when either (a) it is epistemologically 
basic, or (Jb) it has certain syntactical relations to one or more 
epistemologically basic propositions. 

A sentence is "significant" when it results from a verifiable 

sentence S by substituting for one or more words of S other 
words of the same logical type. 

The law of excluded middle will then be asserted to apply to 
every significant sentence. 

But this will require a new definition of "truth". 

We said in the epistemological theory that the truth of a 
"basic" sentence is defined by correspondence with an "experi- 
ence". We may, however, substitute "fact" for "experience", 
and in that case, an unverifiable sentence may be "true" because it 
corresponds with a "fact". In that case, if the law of excluded 
middle is to be retained, we shall have to say that, whenever there 



is a verifiable sentence 



containing a certain 

word "a'*, 
which is verified by the appropriate fact about a, if "^'* is a word 

of the same type as "a'*, 

there is a fact indicated by the Sentence 



*/(^)" ^^ ^"^^^^ ^^ ^ ^^^^ indicated by the sentence "not-/(^) 

Thus the law of excluded middle involves us in much difficult 

If the law of excluded middle is to be retained, we shall have 
to proceed as follows 




is undefined 

(2) Some facts are "experienced". 

(3) Some experienced facts are both "expressed 
cated" by sentences. 




" are words of the same logical type, and 
is a sentence expressing an experienced fact, then either 

(4) If "a" and 

"/(^)" indicates a fact or "not-/(i)" indicates a fact 



Data" are sentences expressing and indicating experienced 

or, we may 

(6) "Verifiable" sentences are those having such syntactical 
relations to data as make them deducible from data 
add, more or less probabte^in relation to data. 

(7) "True" sentences are such as either indicate facts, or have 
the same syntactical relations to sentences indicating facts as 
verifiable sentences have to data. 

On this view, verifiable sentences are a sub-class of true 



seems fairly clear that the law of excluded middle cannot 
be preserved without the metaphysical principle (4) above. 

There are difficulties in both theories of truth. The epistemo- 
logical theory of truth, consistently developed, limits knowledge 
to a degree diat seems excessive, and that is not intended by its 
advocates. The logical theory involves us in metaphysics, and 
has diflSculties (not insuperable) in defining the correspondence 
which it requires for the definition of "truth 

Whichever theory we adopt, it should, I think, be conceded 

that meaning is limited to experience, but significance is not. 
As regards meaning: we may, on the usual grounds, ignore 




words that have a dictionary definition, and confine ourselves 
to words of which the definition is ostensive. Now it is obvious 
that an ostensive definition must depend upon experience* 

Hume's principle, '*no idea without an antecedent impression 
certainly applies to learning the meaning of object-words 
our previous discussions have been correct, it applies also to 
logical words; "not" must derive its meaning from experiences 
of rejection, and "or" from experiences of hesitation. Thus no 
essential word in our vocabulary can have a meaning inde- 
pendent of experience. Indeed any word that / can understand 
has a meaning derived from my experience. 

As regards significance : this transcends my personal experience 
whenever I receive information; it transcends the experience of 
all mankind in works of fiction. We experience "Hamlet", not 
Hamlet; but our emotions in reading the play have to do with 
Hamlet, not with "Hamlet". "Hamlet" is a word of six letters; 
whether it should be or not be is a question of little interest, 
and it certainly could not make its quietus with a bare bodkin. 
Thus the play "Hamlet" consists entirely of false propositions, 
which transcend experience, but which are certainly significant. 

since they can arouse emotions. When I say that our emotions 
are about Hamlet, not "Hamlet", I must qualify this statement: 
they are really not about anything, but we think they are about 
the man named "Hamlet". The propositions in the play are false 
because there was no such man; they are significant because we 
know from experience the noise "Hamlet", the meaning 
"name" and the meaning of "man". The fundamental falsehood 
in the play is the proposition: the noise "Hamlet" is a name. 
(Let no one make the irrelevant remark that perhaps there was 
once a Prince of Denmark called "Hamlet".) 

Our emotions about Hamlet do not involve belief. But emo- 
tions accompanied by belief can occur in very similar circum 

stances. St. Veronica owes her supposed existence to a verbal 
misunderstanding, but is none the less capable of being an 
object of veneration. In like manner the Romans revered 
Romulus, the Chinese revered Yao and Shun, and the British 



revered King Arthur, though all these worthies were literary 

We saw in Chapter XIV that a belief such as * 'y ^^ are ho t* * 
involves a variable in its complete expression. Can we say that 
every belief of mine which transcends my personal experience 
involves at least one variable.^ Let us take an instance as un- 
favourable as possible^to this hj^othesis. Suppose I am standing 
with a friend looking at a crowd. My friend says "there's Jones 
I believe him, but cannot see Jones, whom I am supposing known 


to me as well as to my friend. I shall suppose that my friend 
and I attach the same meaning to the word "Jones"; fortunately 
it is not necessary in the present connection to discuss what this 
meaning is. The word "there" is, for our purposes, the crucial 
one. As used by my friend, it is a proper name for a certain 
visual direction. (We have discussed in Chapter VII the sense 
in which "there", which is an egocentric particular, can be 
regarded as a proper name.) My friend may elucidate the word 

"there" by pointing; this enables me to know approximately 

what direction he is calling "there". But whatever he may do or 
say, the word "there", to^me, is not a proper name, but only a 
more or less vague description. If I see Jones, I may say: "oh 

yes, there he is". I am then uttering a proposition which my 
friend's statement had failed to convey to me. The heard word 
"there" as used by my friend means to me only "somewhere 
within a certain region", and thus involves a variable. 

Let us try to define the word "experience", which is often 
used very loosely. It has different, though connected, meanings 
in different connections. Let us begin with a linguistic definition. 

Linguistically, a word has a meaning which lies within "ex- 

perience" if it has an ostensive definition. The word 'Hamlet' 
does not have a meaning which lies within experience, because I 
cannot point to Hamlet. But the word " *Hamlet' " does have a 
meaning which lies within experience, because it iheans the 
word *Hamlet', which 1 can point to. When a word has an 
ostensive definition, we will call it an "experience-word". Among 
such words are included all genuine proper names,all theapparatus 



of predicates and relations that have no dictionary definitions 
and also some few logical words as expressing states of mind 
such as rejection or hesitation. 

The above definition is satisfactory while we are concerned 
with language, but elsewhere is too narrow. Understanding a 
word in virtue of an ostensive definition is merely one kind of 
habit, and ' 

experience" may, in some of its uses, be identified 

that the 

with "habit". Or, to speak more exactly, we may say 

difference between an event which is "experienced" and one 
which merely occurs is that the former, but not the latter, gives 
rise to a habit. 

The above definition has bpth advantages and disadvantages. 
In considering what these are, we must remember that the main 
question we are concerned with is whether we have any know- 
ledge as to what is not experienced, and that it is in order to 
make this question precise that we are seeking a definition of 

Now every one would agree that 

experience" is 

experience . 

confined to animals, and perhaps plants, but is certainly not to be 
found in inanimate matter. Most people, if asked to mention the 

diiference between a man and a stone, would probably reply that 
the man, but not the stone, is "conscious". They would probably 
concede that a dog is "conscious", but would be doubtful about 
an oyster. If asked what they mean by "conscious", they would 
hesitate, and perhaps in the end would say that they mean "aware 
of what is happening about us". This would lead us to the dis- 
cussion of perception and its relation to knowledge. People do 


of the temperature, or a 




not say that a thermometer is 

galvanometer of an electric current. Thus we find that 

the term is commonly used, involves something more 
or less of the nature of memory, and this something we may 
identify with habit. In any case, habit is what mainly distinguishes 
the behaviour of animals from that of inanimate matter. 

ness", as 

Reverting to our definition of 



we may observe 

that an event which we are said to 




must connnue 

to have effects after it has ceased, whereas an event which merely 
happens exhausts its effects in the moment of its happening. As 




it stands, however, this is lacking in precision. Every event has 
indirect effects to the end of time, and no event has direct effects 
except at the moment. "Habit'* is a concept which is intermediate 

is to 

between complete ignorance and complete knowledge, 
be supposed that, if our knowledge were adequate, the behaviour 
of living bodies could be reduced to physics, and habit would 
be reduced to effects on the brain which might be compared to 
water-courses. The route taken by water in flowing down a 
hillside is different from what it would be if no rain had ever 
fallen there before ; in this sense, every river may be regarded as 
embodying a habit. Nevertheless, since we can understand the 
effect of each rainfall in digging a deeper channel, we have no 
occasion to use the notion of habit in this connection. If we had 
equal knowledge of the brain, it is to be supposed that we could 
equally dispense with habit in explaining animal behaviour* But 
this would be only in the sense in which the law of gravitation 
enables us to dispense with Kepler's laws : habit would be deduced, 
not assumed, and in being deduced would be shown to be not a 
wholly accurate law. Kepler could not explain why planetary 
orbits are not exact ellipses, and similar limitations apply to 
theories of animal behaviour which begin with the law of habit. 
In the present state of our knowledge, however, we cannot, 
avoid using the notion of habit; the best we can do is to remember 
that "habit'*, and all concepts derived from it, have a certain 
provisional and approximate character. This applies in particular 
to memory. An adequate physiology and psychology would 
deduce memory, as Newtoti deduced Kepler's laws, as something 
approximately true, but subject to calculable and explicable 
inaccuracies. Veridical and misleading memories would be 
brought under the same laws. But this is a distant ideal, and for 
the present we must do our best with concepts which we believe 
to be provisional and not quite accurate. 

With these provisos, we may, I think, accept the view that 

an event is said to be "experienced" when it, or a series of similar 
events of which it is one, gives rise to a habit. It will be observed 
that, according to this defitiition, every event that is remembered 




is experienced. An event may, however, be experienced without 
being remembered, I might know by experience that fire bums 
without being able to recollect any particular occasion on which 
I had been burnt. In that case the occasions on which I had been 
burnt would have been experienced but not remembered. 

Let us now try, first, to state positively the relation of empirical 
knowledge to experience, as it results from our previous dis- 
cussions. When this has been done, we can proceed to defend our 
view against those of certain other philosophers. 

Dependence upon my experience is complete in the case 
all beliefs in the verbal expression of which there are no variables, 
i.e. no such words as "all" or "some". Such beliefs must express 
my perceptive experience, the only extension being that the 
experience may be recollected. The experience concerned must 
be mine and no one else's. Everything that I learn from others 
involves variables, as we saw in discussing the man who says 
"there's Jones". In such a case, the belief conveyed to the auditor 
is never that expressed by the speaker, though it may, in favourable 
cases, be logically deducible from it. When a man, in my hearing, 
makes a statement "/a'*, where "a" is the name of something 
that I have not experienced, if I believe him I believe, not "/a" 
(since for me "a" is not a name), but "there is an x such that/:;c". 
Such a belief, although it transcends my experience, would not 
be excluded by any of the philosophers who wish to define 
"truth" in terms of "experience". 

may be said: when a man exclaims "there's Jones" and I 
believe him, the cause of my belief is his exclamation, and the 
cause of his exclamation is his perception; therefore my belief 
is still based upon perception, though indirectly. I have no wish 
to deny this, but I want to ask how it is known. In order to bring 
out the point at issue, I shall assume it true that my friend said 
"there's Jones" because he saw Jones, and that I believed Jones 
was there because I heard my friend say so. But unless my friend 

and I are both philosophers, the two words "because" in this 

statement must both be causal, not logical I do not go through 
a process of reasoning in arriving at the belief that Jones is there; 



given the stimulus, the belief arises spontaneously. Nor does my 
friend go through a process of reasoning in passing from the 
percept to the utterance "there's Jones"; this also is spontaneous. 
The causal chain is thus clear: Jones, by reflecting sun light, 
causes a percept in my friend; the percept causes the utterance 
"there's Jones", the utterance causes an auditory percept in me, 
and the auditory percept causes in me the belief "Jones is some- 
where in the neighbourhood". But the question we have to ask 
is : what must I know in order that, as a reflective philosopher, I 
may know that this causal chain affords a ground for my belief? 
I am not now concerned with common sense reasons for doubt. 

such as mirrors, auditory hallucinations, etc. I am willing to 
suppose that everything happened as we naturally think it did, 
and even, to avoid irrelevances, that in all similar cases it has so 
happened. In that case, my beliefs as to the causal antecedents of 
my belief that Jones is in the neighbourhood are true. But true 
belief is not the same thing as knowledge. If I am about to become 

a father, I may believe, on grounds of astrology, that the child 
will be a boy; when the time comes, it may turn out to be a boy; 
but I cannot be said to haye hiown that it would be a boy. The 
question is : is the true belief in the above causal chain any better 
dian the true belief based on astrology ? 

There is one obvious difference. The prophecies based on the 
above causal chain, when they can be tested, turn out to be true; 
whereas astrological prophecies as to the sex of a child will, in a 
series of cases, be false as often as they are true. But the hypo- 
thesis that the light-waves proceeding from Jones, the percept 
and utterance of my friend, and the sound-waves proceeding 
from him to me, are mere auxiliary fictions in the causal inter- 
connection of my percepts, has- the same consequences as the 
realist hypothesis, and is therefore equally tenable if my percepts, 
are the sole ground of my empirical knowledge. 

This, however, is not the main objection. The main objection 
is that, if it is meaningless to suppose that there are unexperienced 
events, the light-waves and sound-waves involved in the realist 
hypothesis are meaningless. Unless we assume a plenum of 




Leibnizian monads, all causation between human beings will 
have to be telepathic: my friend experiences himself saying 
"there's Jones", and after a time, without anything relevant 
having happened meantime, I hear what he has said. This hypo- 
thesis seems preposterous, and yet, if we deny that there can be 
truth about unexperienced events, we shall be forced to adopt it. 
Thus if we assert that it is meaningless to say that there are events 
which no one experiences, we cannot avoid conflicting grossly 
with scientific common sense — ^just as grossly, in fact, as if we 
were solipsists. 

Nevertheless, the hypothesis that only experienced events 
occur is not logically refutable, any more than the solipsist hypo- 
thesis. We need only suppose that, in physics, all those events 
that are not experienced are mere logical fictions, introduced for 
convenience in interconnecting the events that are experienced. 
In this hypothesis, we accept the experiences of others, and there- 
fore admit testimony, but we do not admit unperceived events. 
Let us consider whether anything is to be said in favour of this 
hypothesis from the standpoint of the meaning of "truth". 

The main argument will be derived from the difficulty 
defining the correspondence which is to constitute basic truth in 
cases in which no percept is involved. Between a certain percept 
and the utterance "there*s Jones" there is a causal connection 
which we more or less understand; this connection constitutes 
tlie correspondence in virtue of which the utterance is "true". 
But where no percept is involved, no such simple type of corre- 
spondence is possible. 

It will be remembered, however, that propositions which go 
outside the experience of the speaker always involve variables, 
and that such propositions necessarily derive their truth (when 
they are true) from a correspondence of a different kind from 
that involved in the case of propositions not involving variables. 
The statement "there are men in Los Angeles" is verified by any 
one of a number of facts, namely that A is there and is a man, 
that B is there, etc. No one of these has any special claim to be 
the verifier of the statement. On purely logical grounds, therefore, 



we should not expect the same kind of correspondence, or truth 
of the same "type", in the case of unperceived events as in that 
of events that are perceived. 

Let us take the statement "you are hot", which we considered 
in Chapters XV and XVI. We decided that, in order to interpret 
this, we must be able to describe some occurrence x which is 
part of your present biography but of no one else's, and then 
add "hotness is comp resent with x^\ In order to make sure that x 
belongs to no other biography, we must use some quality of the 
sort employed in defining spatio-temporal position. We suggested 
your percept of your body, but your percept of my body would 
do equally well. By means of the laws of perspective and my 
location of my percept of your body among my other percepts 

I can approximately infer the character of your visual percept of 

your body. If R is the perspective relation that I use in this 

inference, while a is my visual percept of your body and C is 
the relation of compresence, "you are hot" means "there is an x 

which has the relation R to a and the relation C to hotness". 
Here all the constants — ^i.e. all the terms except x—ztt derived 
from experience. The correspondence with fact (supposing the 
proposition true) is of the only kind possible for existence 

propositions. From "I am hot" I can infer "some one is hot"; 
this has the same sort of correspondence with fact as "you are 
hot" on the above interpretation. The difference lies not in the 
kind of correspondence, but in the circumstance that in the one 
case the verifying fact is a percept of my own and in the other 

it is not 

Let us now take a statement about something that no one 

experiences, such as sound-waves or light-waves. I am not 
arguing that such statements can be known to be true ; I am only 
concerned to assign a significance to them. Suppose you and ^ 
are at a considerable distance from each other along some 
measured road. You fire a pistol, and I first see the smoke and 
then hear the report. You move along the road while I stand still; 
I find by experiment that the time between my seeing the flash 

and hearing the report is proportional to your distance from me. 



So far I have introduced nothing that transcends my experience. 
Your movement may be taken as the movement of my percept 
of you, your position on the road may be taken as the position 
of my percept of you on my percept of the road, and your dis- 
tance from me may be taken to be the number of percepts of 
measuring-posts between my percept of my body and my percept 
of yours. Equality of distance between successive measuring 
posts is easily interpreted subjectively, since the space con- 
cerned may be taken to be the space of my percepts, not physical 


The essential transition involved is that from perceptual to 
physical space. To eliminate testimony, which is not essential 

in the present connection, I shall suppose, not that you fire a 
pistol, but that I have placed a series of time-bombs at the various 
measuring posts, and that I measure the intervals between seeing 
and hearing the various explosions. What is the nature of the 
inference from these subjective experiences to physical space? 

It must be understood that I am not discussing any inference 
performed by common sense. Common sense believes in naive 
realism, and makes no distinction between physical and per- 
ceptual space. Many philosophers, although they have realized 
that naive realism is untenable, nevertheless retain some opinions 
logically connected with it, more particularly in diis matter 
different kinds of space. The question that I am discussing is this: 
having realized all that is implied in the rejection of naive realism 
how can we enunciate the hypotliesis that there is physical space 
and what sort of principle would (if true) justify us in believing 
this hypothesis r 

Part, at least, of the hypothesis involved is that a cause and its 
effect, if separated by a finite time-intervai, must be connected 
by a continuous intermediate causal cliain. There is evidently a 
causal relation between seeing and hearing the explosion; when 

am on the spot, they arc simultaneous; we therefore assume 
that, when they are not simultaneous, there has been a series of 
intermediate occurrences, which, however, were not perceived 
and are therefore not in percej)tual space. This point of view is 







reinforced by the discovery that light, as well as sound, travels 
with a finite velocity* 

We may therefore take, as a principle which will serve for 

the purposes of discussion: if, in my experience, an event of 
kind A is always followed, after a finite interval, by an event of 


kind B, there are intermediate events which interconnect them. 

Some such principle is certainly involved in scientific procedure 
its exact form is, for our purposes, unimportant. 

This is an instance of a more general question: given an 

existence-proposition of which I do not experience any verifier, 
what is involved in supposing that I can know it ? The problem 
is, in part, not essentially different in the case of "there are sound- 
waves in air" and "there are people in Semipalatinsk". In the 

latter case, it is true, I could experience verifiers by taking a 
journey, whereas in the former case I could not. But so long as I 
do not actually take the journey, this difference is not decisive. 
Each proposition is believed, not on sensible evidence alone, but 
on a combination of sensible evidence with some non-demon- 
strative form of inference. 

Perhaps all non-demonstrative inferences can be reduced to 
induction ? The argument would be as follows : I infer people in 
Semipalatinsk, and subsequently verify my inference. Many 
instances of such verification make me feel confidence in similar 
inferences even when unverified. But is it possible for an inductive 
inference to be not merely unverified, but unverifiable? This is 
the case of sound-waves, which can never be perceived. Do these 
require some further principle than induction 

might be said: the hypothesis of sound-waves enables us 
to predict occurrences which are verifiable, and thus receives 
indirect inductive confirmation. This depends upon the general 
assumption that, as a rule, untrue hypotheses will have some 
consequences that can be shown by experience to be false. 

At this point, there is a substantial difference between hypo- 
theses about what can be experienced and hypotheses about what 
cannot. The hypothesis that whenever I have seen an explosion 

shall soon hear a noise is one which, if false, will sooner or 




later be proved false by my experience. But the liypothesis that 

the sound reaches me by means of siamd-waves niiglu be false 
without ever leading to any conscquerice that experience would 
show to be false; we can suppose that the sound-waves are a 
convenient fiction, and tfte sounds which I hear occur as if hornt 

sound-waves, but in fact without non-sensible antecedents. 


This hypothesis cannot be rejected on grounds of induction; if 
it is to be rejected^ it must be on grounds of some other kind. 

for example^ on the basis ai the principle of continuity mentioned 

We may distinguish four assemblages of events: (i) those 

that I experience, (z) tltose in which I believe on the basis of 

testimony, (3) all thi^se ever experienced by human beings, 

^ u ^ ^ ^ m ^ ^\UW ,fk M teak ^.^^ ..^^^ \ 

(4) those assumed in physics, 01 these I know empirically that 
portion of (1) that I now perceive or remember; from these I can 
arrive at my future or forgotten experiences by assuming induc- 
tion, I can arrive at (2) by means of analogy, if I assume that 

speecli or writing which I hear or see **means** what it would if 
I spoke or wrote it. Given this assumption^ i can by induction 
arrive at (3)- But how about (4) 


It may be said; I believe in (4) because it leads to a harmonious 
body of theory, at all points consisieni with (1), (2), and (3) 

and giving a simpler statement of the laws governing the occur 


rence of (i), {%% and {%% than can be obtained otherwise* As to 
thisj however, it should be said that (1) alone, or (z) alone^ or 

(3) alone, allows an equally harmonious theory by merely 

supposing the events in excluded groups to be convenient 


alcmej (2) alone, (3) alone, or 

lions* The four 

(4) — ^are empirically indistinguishable, and if we are 10 adopt 

any except (1) alone we must do so on the basis i>f some non- 
demonstiable principle of inference^ whicli cannot be rendered 
either probable or improbable by any empirical evidence* Sin<^ 

no one accepts (1) alone, I conclude that there are no true em 
piricistSj and that empiricism^ though not logically refutable, is 
in fact believed by no one. 
The argument that an unverifiable extstence-proposiiion, such 



as those of physics, is unmeaning, is to be rejected. Every con- 
stant in sucli a proposition has a meaning derived from experience. 
Many such propositions — e.g. **the good, when they die, go to 
heaven" — have a powerful effect both on emotion and on action. 
Their type of relation to fact, when they are true, is just the same 
as in the case of verifiable existence-propositions or general pro- 

positions- I conclude that there is no ground in the analysis of 
significance for rejecting them, and that empiricism affords only 
such grounds against (4) as apply equally against (2) and (3), 

therefore accept the law of excluded middle without quali- 

To sum up the result of this long discussion : what we called 

the epistemological theory of truth, if taken seriously, confines 

**truth'* to propositions asserting what I now perceive or 
remember. Since no one is willing to adopt so narrow a theory, 
we are driven to the logical theory of truth, involving the possi- 
bility of events that no one experiences and of propositions that 
are true although there can never be any evidence in their favour. 


Facts are wider (at least possibly) than experiences. A "veri- 
fiable" proposition is on^Jiaving a certain kind of correspondence 
with an experience; a **true" proposition is one having exactly 
the same kind of correspondence with a fact — except that the 
simplest type of correspondence, that which occurs in judgments 
of perception, is impossible in the case of all other judgments, 
since these involve variables. Since an experience is a fact, veri- 
fiable propositions are truej but there is no reason to suppose 
that all true propositions are verifiable- If, however, we assert 
positively that there are true propositions that are not verifiable, 
we abandon pure empiricism. Pure empiricism, finally, is believed 
by no one, and if we are to retain beliefs that we all regard as 
valid, we must allow principles of inference which are neither 
demonstrative nor derivable from experience. 


Chapter XXII 


whit may have been thoudu a 

In Chapter XXI^ I 

parody of empiricism, .and decided againsi it. I did not mean 

to decide against all pcmbk* i'tmns of cmpiricisnij but only to 

bring out certain implicatiuns r4 whin h generally accepted as 
scientific knowledge, whicli seem to me to be insufBciently 
realized by mosi modern empiricists. It will serve to give precision 
to %vhat I am asnerting to ccnnpare it with opitiiunn widi which 
am very nearly in agreement. ¥w this purpose, I shall^ in die 
presient chapter^ examine in detail certain parts of Carnap*$ 
**TestafaiHty and Meaning**.* This is an itnpi^rtani and careful 
analysts; in pariicuhr^ his dit^itnction between **Reduction'* and 

ion*' throws much hujht on»tfie theory of scientific 

method* In so far as I have any dinvigrvenKnu with Carnap*s 

views, this arises ahnost entirely from rnv belief that lie begins 

rather too late in his analyses^ and that certain prior problems, 
to which the present work is mainly devoted, are niore important 

than he woidd be inclined to admit. This opinion I shall now 
proceed to defend controversially. 

Carnap begins %viih a discussion of the relation Ix»tween the 
three concepts **meamng'\ **truth*\ and **veritiabi!ify*\ (What 
he calls ^'meaning'* is what 1 have called **signitkance**» i*e* it 
is a property of sentences.) He says : 


Two chief problems of the theory of knowledge are tiic 

question ot meaning and tlie questii^n of verification. The first 

question asks nnder what conditions a sentence has meanings in 
the sense of cognitive, factual meanii^g. The sectnid one asks 
how we get to know somethings how we can find ont whether a 


PMittAop/iy (s/'^uVmv, vols, in ami h\ j^|f* md «9|7^ 



given sentence is true or false. The second question presupposes 
the first one. Obviously we must understand a sentence, i.e. we 
must know its meaning, before we can try to find out whether it 
is true or not. But, from the point of view of empiricism, there 
is a still closer connection between the two problems. In a certain 
sense, there is only one answer to the two questions. If we knew 
what it would be for a given sentence to be found true then we 
would know what its meaning is. And if for two sentences the 
conditions under which we would have to take them as true 
are the same, then they have the same meaning. Thus the meaning 
of a sentence is in a certain sense identical with the way we 
determine its truth or falsehood; and a sentence has meaning only 
if such a determination is possible." 

Carnap regards as oversimplified the thesis **that a sentence is 
meaningful if and only if it is verifiable, and that its meaning is 
the method of its verification". This formulation, he says, "led 
to a too narrow restriction of scientific language, excluding not 
only metaphysical sentences but also certain scientific sentences 
having factual meaning. Our present task could therefore be 
formulated as that of a jnodification of the requirement of veri 
fiability. It is a question of a modification, not of an entire rejection 

of that requirement. 

The cruder view is stated, for example, by Schlick:* "Stating 
the meaning of a sentence amounts to stating the rules according 
to which the sentence is to be used, and this is the same as asking 
the way in which it can be verified (or falsified). The meaning of 
a proposition is the method of its verification [my italics]. There is 

no way of understanding any meaning without ultimate reference 
to ostensive definitions, and this means, in an obvious sense, 



reference to 'experience' or 'possibility of verification*/* 

In this passage, Schlick falls into a fallacy from failure to dis- 
tinguish between words and sentences* All necessary words^ as 
we have seen, have ostensive definitions, and are thus dependent 
on experience for their meaning. But it is of the essence of the 
use of language that we can understand a sentence correctly 

a|r 4« 

MeaninK and Verification", Philosophical Review, vol. 4S, J^Y, m^ 



compounded out of words that we understand, even if we have 
never had any experience corresponding to the sentence as a 
whole. Fiction, history, and all giving of information depend 
upon this property of language* Stated formally: given the 
experience necessary for the understanding of the name "a" and 

the predicate "P'\ we can understand the sentence "a has the 
predicate P" without the need of any experience corresponding 

to this sentence; and when I say that we can understand the 
sentence, I do not mean that we know how to jfind out whether 
it is true. If you say "Mars contains inhabitants as mad and 
wicked as those of our planet", I understand you, but I do not 
know how to find out whether what you say is true. 

Again, when it is said that "the meaning of a proposition is 
the method of its verification", this omits the propositions that 
are most nearly certain, namely judgments of perception. For 
these there is no "method of verification", since it is they that 
constitute the verification of all other empirical propositions that 
can be in any degree known. If Schlick were right, we should 
be committed to an endless regress, for propositions are verified 
by means of other propositions, which, irl turn, must derive their 
meaning from the way in which they are verified by yet other 
propositions, and so on ad mjinitum* All those who make "veri- 
fication" fundamental overlook the real problem, which is the 
reUtion between words and non-verbal occurrences in judgments 
of perception. 

The process of verification is never sufficiently examined by 
those who make it fundamental In its simplest form, it occurs 
when I first expect an event and then perceive it. But if an event 


occurs without my having first expected it, I am just as capable 
of perceiving it and forming a judgment of perception about it; 
yet in this case there is no process of verification. Verification 
confirms the more doubtful by means of the less doubtful, and 
is therefore essentially inapplicable to the least doubtful, viz. 
judgments of perception. 

Let us now return to Carnap. He says "if we knew what it 
would be for a given sentence to be found true then we would 



know what its meaning is". Here, on grounds which I have given 
previously, we must distinguish sentences containing variables 
from such as contain only constants. Let us take first the case 
in which there are only constants; consider, for example, some 
subject-predicate sentence *T(a)", where the predicate "P" and 
the name *'a" both have ostensive definitions. This implies that 
I have had experiences w'hich were expressed in sentences "P(^)", 
"P(c)", "P((af)" . • . by means of which I acquired the habit of 
associating "P" with P; it also implies that I have had experiences 
which were expressed in sentences "Q(<2)", "R(a)", "S(a)** . , 
by means of which I acquired the habit of associating **a*' with a. 

But it is assumed that I have never had an experience which 
should express in the sentence "P(a)'\ However, I am supposed 
"to know what it would be for this sentence to be found true'*. 
I do not see what this can mean except that we can imagine the 
percept which would lead us to pronounce the sentence "P(a) 
as a judgment of perception. This is certainly a sufficient condition 



for understanding the sentence, but I am not sure that it is a 
necessary one. For example, if we hear "P(a)" asserted, we may 
act appropriately without any intermediary between hearing and 
acting, and we must then be said to understand the sentence. 

Let us now take the much commoner case in which the sen- 
tence concerned contains at least one variable. According to what 
has been said in previous chapters, it is doubtful whether a pro- 
position which is not a judgment of perception can ever contain 
no variable; thus perhaps the case discussed in the last paragraph 
never occurs. In any case, when it seems to occur the sentence 
concerned will be found, usually if not always, to be an existence- 
sentence: "there is an x such that . . ." 

In the caseof a sentence of the form "there is an Jtrsuch that . . /', 
to say "what it would be for the sentence to be found true" is 
not easy,, and involves another sentence of the same form. Take 
the case of a murder, committed, according to the verdict of the 
coroner's Court, by some person or persons unknown. (We will, 
for simplicity, omit "or persons".) In what sense do we know 
"what it would be for this sentence to be found true"? The 




simplest hypothesis is that some new witness comes forward 

and says he saw the murder committed by Mr. A. I shall omit 
the possibility of perjury. We have thus, while we are considering 
the possibility of a new witness, a whole series of hypothetical 

percepts: B or C or D • . . or Z seeing A do it; A or C or D 

or Z seeing B do it; A or B or D or . . . Z seeing C do 

it; and so on — where A, B, C - . . Z are all the men there are. 

Thus to know what it would be for the sentence to be found 
true is to know what it would be for some man to see some other 
man committing the murder, i.e. to know what is meant by 
another sentence of the same form. 

Speaking generally, the sentence "there is an xsuch that /at'* 
may be found true if ''fa' or **/^*' or *'/c*', or etc, is a judgment 
of perception. The sentence has a multitude of possible verifiers, 
and therefore we cannot, in advance, describe its verification 

except by another existence-sentence. 

At this point, however, it is necessary to recall what we said 
in connection with memory, to the effect that we may, in virtue 
of past perception, know an existence-proposition without 
knowing the definite perceptive proposition which existed on the 
occasion that gave rise to our present vague recollection. 

memory is accepted — as I think it must be- — as an independent 
source of knowledge (independent logically, not causally, since 
all memories are causally dependent on previous percepts), then 

a sentence must be considered verified if it either expresses or 
follows from a present recollection. In that case, there will be a 
kind of verification which consists in arriving at an existence- 
proposition expressing a memory-belief. This kind of verifica- 
cation, however, in view of the fallibility of memory, is inferior 
to that by perception, and we shall always endeavour, as far as 
we can, to supplement it by perceptive verification. 

I omit, for the moment, the case of universal propositions such 
as "all men are mortar*. For the moment, I am only concerned 
to show that the phrase "what it would be for a sentence to be 
found true" is one of which the interpretation is far from simple. 

Between the. method that I advocate in theory of knowledge 



and that advocated by Camap (in company with many others), 
there is a diflPerence in starting-point which is very important 
and (I think) insufficiently realized. I start from sentences about 
particular occurrences^ such as "this is red", "that is bright", 
"I-now am hot". The evidence in favour of such a sentence is 
not other sentences, but a non-verbal occurrence; the whole of 

the evidence is contained in a single such occurrence, and nothing 
that happens at any other time or place can confirm or confute 
this evidence. Previous occurrences are concerned causally in my 
use of language: I say "red" because of a habit generated by past 
experiences. But the manner in which the habit was formed is 
irrelevant to the meaning of the word "red", which depends upon 
what the habit w, not upon how it came about. 

Every sentence of the above kind is logically independent of 
all the others, severally and collectively. Whenever, therefore, 
one such sentence is said to increase or diminish the probability 
of another such sentence, this must be in virtue of some principle 
of interconnection, which, if believed, must be believed on evi- 
dence other than that of perception. The most obvious example of 
such a principle is induction. 

The sentences that Calnap has in mind must, in view of what 
he says about them, be of a different kind. Some quotations 

will help to make this clear. 

"We distinguish the testing of a sentence from its confirma- 
tion, thereby understanding a procedure — e.g. the carrying out 
of certain experiments — ^which leads to a confirmation in some 
degree either of the sentence itself or of its negation. We shall 
call a sentence tes table if we know such a method of testing it; 
and we shall call it confirmabk if we know under what conditions 
the sentence would be confirmed" (p. 420). 


predicate *P' of a language L is called observable for an 


organism (e.g. a person) N, if, for suitable arguments, e.g. 'b\ 
is able under suitable circumstances to come to a decision 
with the help of few observations about a full sentence, say 
'V{b)\ i.e. to a confirmation of either 'V{iy or 'not-P(J)' of such 
a high degree that he will either accept or reject *P(i)' " (p. 454)- 




These passages make it obvious that Carnap is thinking of 
sentences having some degree of generality, since various different 
occurrences may have a bearing on their truth or falsehood. In 
the first passage, he speaks of experiments which confirm in some 
degree the sentence or its negation. He does not tell us what it 
is that we learn from each experiment. Yet unless each experi- 
ment taught us somethings it is difficult to see how it could have 
any bearing on the truth or falsehood of the original sentence. 
Further: the original sentence must have had a bearing upon 
events at various different times, since otherwise the experiments, 
which occurred at different times, could not have increased or 
diminished the probability of its truth- The sentence must there- 
fore have had a greater degree of generality than the sentences 
embodying the results of the several experiments. These latter 
therefore, must be of a logically simpler form than the sentence 
which they confirm or confute, and our theory of knowledge 
ought to begin with them rather than with the sentence that they 
are to prove or disprove. 

Very similar remarks apply to the second quotation. Carnap 
speaks of "few observations** as being ^necessary to decide the 
truth of **P(i)". Now if more than one observation is possible 
b must be capable of occurring more than once, and cannot there- 
fore be an event, but must have the character of a universal. I 




am convinced that this consequence is not intended by Carnap, 
but I do not see how it can be avoided^ — except, perhaps, by the 
theory of proper names advocated in Chapter VI, which Carnap 
would be compelled to reject in view of the importance that he 
attaches to space-time. 

Even if we adopt the theory of Chapter VI as to proper names, 
we do not really escape from the difficulty as to repetition. 
Suppose I see, on two different occasions, a given shade of colour 
C* My percept is in each case a complex, from which C has to be 
disengaged by analysis, and if I am to use both occasions to give 

me knowledge of C, I shall need a judgment of identity: "diis 
shade of colour that I see is identical with a certain shade that I 
remember seeing'*. Such a judgment takes me beyond any 



present perception, and cannot have any high degree of certainty. 
Thus on any theory the possibility of repetition, which Carnap 
assumes, involves difficulties which he does not seem to realize, 
and shows that the kind of sentence that he is considering is not 
the kind from which a discussion of empirical evidence ought to 
start, since it is both less simple and less certain than sentences of 
another kind, of which the existence is implied in Carnap's dis- 
cussion, although he does not seem to be aware of this 

All use of language involves a certain universality in fact, but 
not necessarily in knowledge. Consider, for example, the defini- 
tion of "predicate'\ A predicate is a class of similar noises con- 

nected with a certain habit. We may say: *'let P be a class of 
similar noises. Then P is, for a given organism N, a 'predicate' 
if there is a class E of similar events such that the occurrence of 

any member of the class E causes in N an impulse to make a 
noise of the class P". The class of noises P will only have this 

property for N if N has frequently experienced members of E 
and P in conjunction. Repetition and universality, infact^ are of 
the essence of the matter,, for language consists of habits, habit 
involves repetition, and repetition can only be of universals. 
But in knowledge none of this is necessary, since we use language, 
and can use it correctly, without being aware of the process by 

which we acquired it. 

To come to another point : Carnap defines what he means by 
an observable predicate^ but not, in general, what is to be meant 

a sentence of which the truth can be tested by observation. 

For him, a predicate "P" is observable if there is a sentence 
**P(^)" which can be tested by observation; but this does not help 
us to know whether "P(c)" can be tested by observation. I 
should say that, unless there were a number of sentences of the 
form "P(^)" which had already been tested by observation, the 

word *T*' would have no meaning, since the habit that con 
stitutes meaning would not have been generated. What is proper 

matter for observation, I should say, is rather a sentence than a 

* Or, more exactly, a predicate having an ostensive definition. 

> 1 









: ' ,^ 


A ' 



word: *P' arid V may both have a meaning, which must 
derived from experience, but there may be no observation 
bearing on the truth or falsehood of the sentence *P(c)'. Whether 
this is the case, is, to my mind, the important question. And I 
should add that, in the kind of sentence which is fundamental for 
empirical data, only one single occurrence can give any ground 
for asserting or denying *P(<:)', As soon as repetition is possible, 
we have passed beyond what is basic. 

The word "observable'*, like all words involving possibility, 
is dangerous. As it stands, Camap*s definition says that 'P' is 
"observable" if certain observations couIJ occur. But we cannot, 
at the outset, know what observations are possible although they 
do not in fact occur. It seems necessary, therefore, to substitute 
"observed" for "observable", and say that the predicate *P' is 


observed if observations actually occur which help to decide 

about T(^)* for some b. 

Further: Carnap*s definition, as it stands, is purely causal: the 
observations cause the observer to believe P(^) or not-P(i). 
Nothing is said — ^and I do not see how, from his point of view, 
anything can be said — ^to show that^ there is any reason (as 
opposed to cause) why these observations should lead to this 


would thus seem that the definition of an "observable" 

predicate T' reduces to: "A observes *P' if there is a *^* such 
that circumstances lead A to assert 'P(3)' or 'not-P(^)' ". In other 
words, since all A's assertions must be the result of circumstances, 
"A observes T' if A asserts T(i)' or *not-P(^)' ". This makes 
the whole theory come to nothing. 

Throughout the above discussion, I have not been contending 
that what Carnap says is mistaken, but only that there are certain 
prior questions to be considered, and that, while they are ignored, 
the relation of empirical knowledge to non-linguistic occurrences 

cannot be properly understood. It is chiefly in attaching impor 

tance to these prior questions that I differ from the logical 

The most important of these prior questions is : can any tiling 


be learnt, and if so what, from a single experience ? Camap and 
the whole school to which he belongs think of knowledge as 
scientific knowledge, and as beginning with such propositions as 
"metals conduct electricity"* Such propositions clearly require a 
number of observations* But unless each single observation yields 
some knowledge, how can a succession of observations yield 
knowledge? Every induction is based upon a number of pre- 
misses which are more particular than the conclusion: "copper 
conducts electricity" is more particular than "metals conduct 
electricity", and is itself an induction derived from "this is 
copper and conducts electricity", "that is copper and conducts 
electricity", and so on. Each of these is itself an induction, based, 
ultimately, upon a series of single observations. Every single 

observation tells the observer something. It may be difficult to 
express in words exactly what can be learnt from one observation, 
but it is not impossible; I am at one with the logical positivists 
in rejecting the notion of ineffable knowledge. I do not see how 
it can be denied that our knowledge of matters of fact is built 

up, by means of inference, from premisses derived from single 

is because I regard single observations as supplying our 

factual premisses that I cannot admit, in the statement of such 
premisses, the notion of "thing", which involves some degree 
of persistence, and can, therefore, only be derived from a plurality 
of observations. The view of Carnap, which allows the concept 
of "thing" in the statement of factual premisses, seems to me to 
ignore Berkeley and Hume, not to say Heraclitus. You cannot 
step twice into the same river, because fresh waters are continually 
flowing in upon you; but the difference between a river and a 
table is only a matter of degree. Carnap might admit that a river 
is not a "thing"; the same arguments should convince him that 

a table is not a "thing". 

Carnap advances an argument, which must be examined in 
this connection, to prove that "there is no fundamental difference 
between a universal sentence and a particular sentence with regard 
to verifiability but only a difference in degree". His argument is: 







Take for instance the following sentence: There is a white 
sheet of paper on this table/ In order to ascertain whether this 
thing is paper, we make a set of simple observations and then 
if there still remains some doubt, we may make some physical 
and chemical experiments. Here as well as in the case of the law 
we try to examine sentences which we infer from the sentence in 
question. These inferred sentences are predictions about future 
observations. The number of such predictions which we can derive 
from the sentence given is infinite; and therefore the sentence 
can never be completely verified." 

The question of certainty or complete verification is not the 
one I wish to discuss. In all the arguments known to me on this 
subject, except those of Reichenbach, the question whether a 
proposition is certain is mixed up with the question whether it 

is a factual premiss. I am prepared to admit that what we take 
to be perceptive judgments, like recollections (though in a less 
degree), are fallible; this, however, is irrelevant to the question: 
"what form ought we to give to the propositions that we admit 
as factual premisses ?" 

It is obvious that, if nothing can be learnt from one observa- 
tion, then nothing can be learnt from many observations. There- 
fore our first question must be: "what can be learnt from one 
observation i^" What can be learnt from one observation cannot 
contain words applicable to classes of things, such as "paper" 
and "table". We saw in an earlier chapter that "there is a dog" 
cannot be a factual premiss, but "there is a canoid patch of colour" 

can be.* A factual premiss must not contain words which are 
condensed inductions, such as **dog", "paper", "table". 

Carnap's argument, quoted above, really involves appeal to 
such factual premisses as I consider essential, but msJces this 
appeal by the way, and as though it were unimportant "In order 
to ascertain whether this thing is paper, we m^e a set of simple 
observations." What do we learn from any one of these obser- 
vations.^ On this point Camap is silent. Again he says: "We try 
to examine sentences which we infer from the sentence in question. 

♦ It is assumed that **canoid" is v$ed in defining *Mog*V not vice versa. 



These inferred sentences are predictions about future observa- 

" This admits that sentences are possible which state what 



is to be learnt from a single observation, and makes it obvious 
that such sentences give the factual premisses from which we 
infer that "this is paper 

As regards the "certainty" of factual premisses, what is to be 
said is as follows. 

First: we give to our factual premisses such a form that no 
two groups of them can be mutually inconsistent, and also no 
one such premiss can be rendered in any degree probable or im- 
probable by any number of others* The interconnecting of factual 
premisses, by means of which they are made to confirm or dis- 
confirm each other, depends upon principles of inference, notably 
induction, which are never demonstrative, which yield only 

probabilities, and which, 

therefore, are not disproved when 

what they show to be probable does not happen. 

Second : the whole of the reason for believing a factual premiss, 
in so far as it is a premiss, is the event to which it refers. The 

evidence for it 



is to say, IS a unique occurrence, not a 

belief; the evidence is complete at 

sentence or propositioil^or 

the moment of the occurrence, was previously non-existent, and 

cannot afterwards be strengthened by any further evidence. 

Third: if we are to hold, as many philosophers do, that a 
factual premiss may be rejected on the basis of later evidence, 
this must be because we accept a priori non-demonstrative forms 
of inference, which experience can neither confirm nor confute, 
but which we regard, in some circumstances, as more certain 
than the evidence of the senses. 


factual premisses may not be certain, but there is 

nothing more certain by which they can be shown to be false 


Chapter XXIII 


It will be remembered that, at the beginning of Chapter XXI 


four theories of truth were distinguished, of which I advocate 
the fourth, which is the correspondence theory. The third, that 
of coherence, was discussed and rejected in Chapter X. The 
second, which substitutes "probability" for '*truth", has two 
forms, in one of which I can accept it, while in the other I must 
regard it as mistaken. In the form in which it merely says that 
we are never quite certain that a given proposition, expressed 
in words, is true, I accept it; but in the form in which it contends 

that the concept "truth'* is an unnecessary one, I reject it. It 
seems to me that " ^p* is probable" is strictly equivalent to " /? 
is true* is probable'*, and that when we say " /?' is probable", 

we need some probability that this statement is true. I see no 
reason why an advocate of probability, as all that is practically 
attainable, should reject "truth" as it appears in the above state- 
ments. I shall therefore not controvert Professor Reichenbach's 
views, since I believe that, by a small modification, they can be 
rendered consistent with my own. 

The first of our four theories, on the contrary, differs radically 
from the theory that I advocate, and must therefore be discussed. 
This is the theory of Dr, Dewey, according to which "warranted 
assertibility" should take the place of "truth*'. I 'have already 
discussed this theory in The Philosophy of John Dewey ^ which 

is Volume I of "The Library of Living Philosophies". The 
reader is referred to this volume for detail and, what is more 

, •,**«, 

important, for Dr. Dewey's answers to my objections. In the 
present chapter I wish to confine myself to the general principle, 
and to consider it as uncontroversially as is compatible with 
giving my reasons for rejecting it. 


appears from Dr. Dewey's reply in the above-mentioned 
volume that I have unintentionally misunderstood and parodied 
his opinions. I am most anxious to avoid doing so if I possibly 

can, the more so as I am convinced that there is an important 
difference between his views and mine, which will not be 


elicited unless we can understand each other. It is because the 
difference goes deep that it is difficult to find words which both 
sides can accept as a fair statement of the issue. This, however 
is what I must attempt. 

So far as I can understand Dr. Dewey, his theory is, in oudine, 
as follows. Among the various kinds of activities in which man- 
kind can engage, there is one called "inquiry", of which the 

general purpose, like that of many other kinds of activity, is to 
increase the mutual adaptation of men and their environment. 
Inquiry uses "assertions" as its tools, and assertions are "war- 
ranted" in so far as they produce the desired results. But in 
inquiry, as in any other practical operation, better tools may, 
from time to time, be invented, and the old ones are then dis- 
carded. Indeed, just as machines can enable us to make better 
machines, so the temporary results of an inquiry may be the 
very means which lead to better results. In this process there 
is no finality, and therefore no assertion is warranted for all 
time, but only at a given stage of inquiry. "Truth" as a static 
concept is therefore to be discarded. 

The following passage in Dr. Dewey's reply to me (Joe. cit.^ 
p. 573) may serve to elucidate his point of view: 

"The exclusive devotion of Mr. Russell to discourse is mani- 
fested in his assumption that propositions are the subject-matter 
of inquiry, a view assumed so unconsciously that it is taken for 

granted that Peirce and I likewise assume it. But according to 
our view — ^and according to that of any thorough-going empiri- 
cist — things and events are the materials and object of inquiry, 
and propositions are means in inquiry, so that as conclusions of 
a given inquiry they become means of carrying on further 
inquiries. Like other means they are modified and improved in 
the course of use. Given the beliefs (I) that propositions are 



from tlie start the objects of inquiry and (il) that all propositions 

have either tnuh or falsity as tlicir inherent property^ and (III) 

*n read tliese two assurnpiitnis into theories— like Pcirce's and 

mine— which deny htnh of thenu and ilie product is just the 
doctrinal confusit>!t that Hunseli finds in wliat we have said/' 
Firsts a few word^ oi perstmal explanation. Any reader 

the present work uill, I hope, Ix* ci^nvinced that I th not make 

pmppsimm the utiinwte subject-'matter ai in<|uiry, since my 
probienii ha*t been, throtight.iu!, the relaticnt between i:ymts and 

that ihev cause men ut assert, I do not* it is 


true, regard ddm^s as the tibfecr u( inc|uiry^ since I hold them 
to be a metaphysical delusion; hni as regards i'%%*ms I do not, 
on finis pcnnt, cii^agree with I)r* Dewey. Again; as regards 

scientific hvpotlieses, nueli as quatuunt thenrv <^r the law 

gravitation^ I am wiliinji; (with stnne qtiaUticatitms) to accept 

hi$ view, but I regard all sucfi iivpt^these'S as a precarious super- 
structure buili oit a foundatioit c»f simpler and less dubious beliefs, 
and i do ntit tiitd^ in Dr. DewTv^s ^^x^rkn, what seems to me an 

adecjuaie disctis>iiun <jf tisis foundatian. 

As to trtith and faisehooeL I shonlJ iniernrei the facts as 

regards inquiries and changing hypotheses somewhat differently* 

I should say that imjuiry lx*gins^ as a ryk% with an assertion that 
is vague and ctnnplex^ but rephtees it^ wlien it ean^ by a number 

of separate assertii^ns each of wliich is less vaigue and less com- 

ex than the original assertion, A contple?^ assertion may be 
analysable into several^ siime true^ some false; a vague assertion 

may be true or false^ but it is often neither* **An elephant is 

smaller than a mouse*' is vague^ and yet defmiiely false; but 
**a rabbit is smaller than a rat** is nut definitely either true or 

false, because some young rabbits are smaller than some old 

rats. When Newion*s theory o( gravitation was replaced 
Einstein's, a certain vagueness in Newton's concept of accelerS' 
tion was removed^ but almost all the assertions imp 

Newton's theory remained tmt\ I should say that this is m 
illustration of what always liappens when an old theory gives 
way to a better one: the old assertions failed to k* definitely 

J 'flW^PHr 





or false, both because 





not see how 

two ideals 

many being 



yere many masquerading 
;rue and some false, 
mprovement except in terms 
and truth. 

One difficulty^ to my mindj in 
ay the question: what is the goal of inquiry 

aim, is not the attainment of truth^ but presumably some kind 
of harmony between the inquirer and his environment. 


Dewey's theory, is raised 

raised this question 

(in the above-mentioned volume) 
but have not seen any answer to it. Other activities, such as 
building houses or printing newspapers or manufacturing bombs, 
have recognizable purposes. In regard to them, the difference 
between a good tool and a bad one is obvious: a good tool 

minimizes the labour involved in achieving the purpose. But 




is neutral as between different aims: whitever we wish 

to do, some degree of inquiry is necessary as a preliminary 

wish to telephone to a friend, I must inquire his number of 

the telephone book, taking care to use the most recent edition, 



since its truths are not etegrnal If I wish to govern the country 
must inquire in previously unfamiliar circles as to how to 
become a political boss» If I wish to build ships, either I or some 
one in my employ must inquire into hydrostatics. If I wish to 

destroy democracy, I must inquire into crowd psychology. And 
so on. The question is : what happens as the result of my inquiry ? 

Dn Dewey rejects the traditional answer, that I come to know 
something, and that, as a consequence of my knowledge, my 
actions are more successful He eliminates the intermediate stage 
of "knowing*^ and says that the only essential result of successful 

inquiry is 


Taking man as he appears to science, and not as he may appear 
to a Cartesian sceotic, there are here two questions to be dis- 




believing **true'' 



sort of psychological occurrence is to be 
as a **believing" ? Second, is there any relation between 

and its environment which allows us to call the 
? To each of these questions I have tried to give 



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1 7 



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1 1 I 


f1 1 











1 1 


I \ 

















f !l 


• i ^ I'. 'V -'--i*. 


an answer in previous chapters. If there are such occurrences 
as " belie vings* ' , which seems undeniable, the question is: can 
they be divided into two classes, the "true" and the "false"? 
Or, if not, can they be so analysed that their constituents can 
be divided into these two classes ? If either of these questions 
is answered in the affirmative, is the distinction between "true" 
and "false" to be found in the success or failure of the effects 
of believings, or is it to be found in some other relation which 
they may have to relevant occurrences ? 

I am prepared to admit that a belief as a whole may fail to be 
"true" or "false" because it is compounded of several, some true, 

and some false. I am also prepared to admit that some beliefs 
fail, through vagueness, to be either true or false, though others, 
in spite of vagueness, are either true or false. Further than this 
I cannot go towards agreement with Dr. Dewey. 

n Dr. Dewey's view, a belief is "warranted" if, as a tool, 
it is useful in some activity, i.e. if it is a cause of satisfaction of 
desire. This, at least, would have seemed to me to be his opinion. 
But he points out {loc. clt.y p. 571) that consequences are only 

to be accepted as tests of validity ''provided these consequences 
are operationally instituted and are such as to resolve the specific 
problem evoking the operations" [his italics]. The second half 
of diis proviso is clear in its meaning.. If I go to a place under 
the mistaken belief that my long-lost uncle lives there, but on 
the way I meet my long-lost aunt, and in consequence she leaves 
me her fortune, that does not prove that "my long-lost uncle 
lives there" had "warranted assertibility". But the first half of 
the proviso, which insists that the consequences must be "opera- 
tionally instituted", is one of which the meaning remains to me 
somewhat obscure. The passage in Dr. Dewey's Logic (Preface, 
. iv) where the phrase occurs does not elucidate it. But in his 

reply to me {loc, cit.^ p. 571) there is a passage which I will 

quote in full, as it is designed to remove my errors in inter- 

"The proviso about the kind of consequences that operate 
as tests of validity was inserted as a caution against just the kind 



of interpretation which Mr. Russell gives to my use of con- 
sequences. For it explicitly states that it is necessary that they 

be such as to resolve the specific problem undergoing investigation. 

The interpretation Mr. Russell gives to consequences relates them 
to personal desire. The net outcome is attribution to me of 
generalized wishful thinking as a definition of truth, Mr. Russell 
proceeds first by converting a doubtful situation into a personal 
doubt, although the difference between the two things is re- 

peatedly pointed out by me. I have even repeatedly stated that 
a personal doubt is pathological unless it is a reflection of a 
situation which is problematic. Then by changing doubt into 

private discorhfort, truth is identified with removal of this dis- 
comfort. The only desire that enters, according to my view, is 
desire to resolve as honestly and impartially as possible the prob- 
lem involved in the situation. "Satisfaction*' is satisfaction of the 
conditions prescribed by the problem. Personal satisfaction may 
enter in as it arises when any job is well done according to the 
requirements of the j ob itself; but it does not enter in any way 
into the determination of validity, because, on the contrary, it 
is determined by that validity." 

find this passage very puzzling. Dr. Dewey seems to speak 
as if a doubtful situation could exist without a personal doubter. 
I cannot think that he means this; he cannot intend to say, for 
example, that there were doubtful situations in astronomical and 
geological epochs before there was life. The only way in which 
I can interpret what he says is to suppose that, for him, a "doubt- 
ful situation" is one which arouses doubt, not only in some one 
individual, but in any normal man, or in any man anxious to 
achieve a certain result, or in any scientifically trained observer 
engaged in investigating the situation. Some purpose, i.e. some 
desire, is involved in the idea of a doubtful situation. If my car 
won't go, that creates a doubtful situation if I want it to go, but 
not if I want to leave it where it is. The only way to eliminate 
all reference to actual desire is to make the desire purely hypo- 
thetical: a situation is "doubtful" in relation to a given desire 
if it is not known what, in that situation, must be done to satisfy 



that desire. When I say "it is not known", I must mean, in order 
to avoid the sort of subjectivity that Dn Dewey deprecates, that 
it is not known to those who have the relevant training. Thus 
suppose I find myself in a situation S, and I desire a situation S', 
and I believe (rightly or wrongly) that there is something 
that I could do which would transform S into S', but the experts 
cannot tell me what to do, then S is, in relation to my desire, 
a "doubtfur* situation. 
Eliminating all reference to personal doubt and desire, we may 

now say: S is "doubtful" in relation to S' if mankind do not 
know of any human action A which will transform S into S', 
but also do not know that no such action is possible. The pro- 
cess of inquiry will consist in performing a series of actions 
A, A', A", ... in the hope that one of them will transform S 
into S'. This, of course, implies that S and S' ate both described 
in terms of universals, since, otherwise, neither can occur more 
than once. A, A', A", . . . must also be so described, since we 
wish to arrive at some such statement as: "whenever you are 

in the situation S, and wish to be in the situation S', you can 
secure your desire by performing the action A", where A must 
be a kind of action, since otherwise it 'could only be performed 


Thus when we take Dr. Dewey*s elimination of subjective 
desire seriously, we find that his goal is to discover causal laws 
of the old sort "C causes E", except that C must be a situation 
plus an act, and E another situation. These causal laws, if they 
are to serve their purpose, must be "true" in the very sense that 
Dr. Dewey wishes to abolish. 

One important difference between us arises, I think, from the 
fact that Dr. Dewey is mainly concerned with theories and hypo- 

theses, whereas I am mainly concerned with assertions about 
particular matters of fact- As explained in the preceding chapter, 
I hold that, for any empirical theory of knowledge, the funda 
mental assertions must be concerned with particular matters 
fact, i.e. with single events which only happen once. Unless 
there is something to be learnt from a single event, no hypothesis 







can ever be either confirmed or confuted; but what is to be learnt 
from a single event must itself be incapable of being confirmed 
or confuted by subsequent experience. This whole question of 
how we learn historical facts by experience seems to me to be 
ignored by Dr. Dewey and the school of which he is the leader. 
Take, for instance, the statement "Caesar was assassinated". This 
is true in virtue of a single event which happened long ago; 
nothing that has happened since or will happen in the future 
can in any way affect its truth or falsehood. 

The distinction between truth and knowledge, which was 
emphasized in coimection with the law of excluded middle, is 
relevant at this point. If I wish to "verify" the statement "Caesar 
was assassinated", I can only do so by means oi future events 
consulting books of history, manuscripts, etc. But these are only 
to the purpose as affording evidence of something other than 
themselves. When I make the statement, I do not mean "who- 
ever looks up the encyclopaedia will find certain black marks on 
white paper". My seeing these black marks is a unique event 
on each occasion when I see them : on each occasion I can know 

that I have seen them; from this knowledge I can infer (more 
or less doubtfully) that Caesar was assassinated. But my per- 
ception of the black marks, and my inference from this percep- 
tion, are not what make the assertion about Caesar true. It would 
be true even if I made it without any grounds whatever. It is 
true because of what happened long ago, not because of any- 
thing that I am doing or shall do. 

The broad issue may be stated as follows. Whether we accept 
or reject the words "true" and "false", we are all agreed that 
assertions can be divided into two kinds, sheep and goats. Dr. 
Dewey holds that a sheep may become a goat, and vice versa 
but admits the dichotomy at any given moment : the sheep have 
warranted assertibility" and the goats have not. Dr. Dewey 
holds that the division is to be defined by the effects of assertions 
while I hold, at least as regards empirical assertions, that it is 
to be effected by their causes. An empirical assertion which can 
be known to be true has percepts, or a percept, among its proxi- 








mate or remote causes. But this only applies to knowledge; so 
far as the definition of truth is concerned, causation is only rele- 
vant in conferring meaning upon words. 

The above discussion has been mainly concerned to clarify 
the issue. The grounds of my own opinions have been, for the 
most part, given in previous chapters. 



Chapter XXIV 




am concerned, in this chapter, with propositions of the form 
"P is part of W\ I wish to inquire whether these are ever part 
of the fundamental apparatus of empirical knowledge, or whether 
they are always to be deduced from a definition of the whole W, 
which, incidentally, will mention the part P whenever "P is part 
of W" is true. Something has already been said on this subject 
in Chapters III and VIII, but I wish now to examine it on its 
own account. 

The operation by which, from examination of a whole W 
we arrive at "P is part of W", is called "analysis'*. It has two 
forms: logical analysis, and analysis into spatio-temporal parts. 
One of the matters to be"* considered is the relation between these 
two forms of analysis. 

From the earliest times, many philosophers have objected to 
analysis: they have maintained that analysis is falsification, that 
a whole does not really consist of parts suitably arranged, and 
that, if we mention any part singly, the act of isolation so alters 
it that what we have mentioned is not what is an organic part 

of the whole. 

The principle of atomicity, which we considered in an earlier 
chapter, represents the opposite extreme from that of the monists. 
The principle of atomicity may be said to forbid synthesis. 
Linguistically, it forbids the giving of proper names to complex 
wholes, at any rate when they are recognized to be complex. 

For my part, I reject both these extremes. 

Those who deny the legitimacy of analysis are compelled to 
maintain that there is knowledge not expressible in words. For 
it is difficult to deny that sentences consist of words, and that 



( ♦ 


therefore* sentential uifcrances can be anahscc! into 



verba! uiteraiK-es, If ihis is u^ be clcnicci, ^t is necessary to deny 
that a sentence is a strintx of Wiircis, and in that case it becomes 
stmieihinu inetVable. 

inse, im the other hantl, whn }>cHeve in analvsis, not infre- 

quently ffilknv langtuige too slavisldy; I have been guilty of this 

fauh mvself* There are iuhj wavs in which lan^uase may guide 

m in analysis; cnie is by c<ni>iciering wotth and sentences as 
sensible facts, the otlwt k by amsitlerini^ the dirterent kinds of 
words, as is doiu^ in grammar. Of these the imt^ I should say^ 
is whollv innc)cu*HiH^ while the seanvd, ih<niuh it has its uses, 

^ Tj ■■■* ^ 

very dangertnis^ and a cnpiuus Muarce t)t vjtat 

hcmn with lantinaEe as contptmed of sensible facts* Sen 

fences are con^pi^^sed c4 wi^rtis^ printed words are comp<itsedl 
kfiers* The ntan who has a hmA imntvd eatises separate bits 
" type u> be put tijgether in a certain <irder; yei^ if he is a philo- 

sopher, his !>ook may be saying that tm series of material objects 
can represent thought. N«nv ii may be tfjc case™'! liope it is— *♦ 

that these phikisopiiers have better ideas in their heads than they 

in putting iiiifu their hrmks hm it is quite certain that 

the ideas in their books cm be expressed by series of material 
objects^ fiir, if mn^ the comp*)s$tur!s wtndd find iheir task im- 
possible* Thtnighl, in so far as it is ec>nimwnicabli% cannot have 
any greater cciinplexity than is possessed by the \'arious possible 
kinds of series to Im made out of twenty-six kinds of shapes. 
Shakespeare*s mind may have H-mx v<*ry wcmderful, but our 

of its merits is wbcdiy deriveci from black shapes on 

a while ground* Tiiose w^hn say that wiirds falsify senjiible facts 
forget that words are sensible facts, and that sentences and words 

a$ facts^ arc compased of discrete parts^ which can be separately 

2d, and are so named by every child learning to $peli. It is 

therefore undeniable that mme sensible facts can Ir* analysed into 

The analysis of a printed %vord into letters is easier than the 
analysis of most sensible facts; it is the purpose of print to make 
the analysis easy* But the difference is only one of degree, and 




some natural phenomena invite analysis just as much as print 
does. A black dog in snow, a rainbow, a seagull against a stormy 

sea, are very noticeable. I believe even the most monistic of 
philosophers would notice a tiger, and not stop to argue that 
it could not be validly considered except in relation to its back- 
ground. Analysis of the sensible present occurs almost inevitably 
where there is a sliarp contrast, such as a sudden noise, or black 
against white. Rapid movement, which is very noticeable, comes 

under the same head. In such cases, we become aware, not simply 
of a whole, but of a complex of parts. If this were not the case, 
we should never have acquired the notion of spatio-temporal 

is customary now-a-days to dismiss contemptuously the 
atomic view of sensation as it appears in Hume and his followers. 
We are told that the sensible world is a continuous flux, in which 
divisions are unreal, the work of the mind, purely conceptual, 
and so on. This is said as something obvious, for which only a 
stupid man would demand evidence- Now the word "sensation" 
or "sensible", as is often pointed out, stands for something hypo- 
thetical^ — broadly speaking, for what coulJ be noticed without 
change in the environment or the sense-organs. What is not 
hypothetical is what k noticed, not what could be noticed; and 
what is noticed has, I maintain, just that atomicity and discrete- 
ness which the critics of Hume reject. They do not, as empiricists 
should, Stan from data, but from a world that they have inferred 
from data but use to discredit the kind of thing that can be a 
datum. In theory of knowledge, what is fundamental is noticing, 

not sensation. 

shall take for granted, henceforth, that we can, within a 
perceived whole, perceive parts as interrelated. It is not necessary 
to suppose t!)at the parts are "simple", nor is it clear what this 
supposition would mean. For the purpose of expressing in words 
what we perceive in such a case, the smallest parts that are 

should be given proper names, and then we can state 

how they are related 

Such analysis as I have been considering hitherto is spatio 



temporal, but there is another kind of analysis that raises much 
more difficult problems; it is that which proceeds from con- 
sidering different kinds of words, and which inquires whether 
anything corresponds in the non-verbal world. The matter may 
be put as follows: given a complex whole, there are not only 
parts, but the parts are arranged in a pattern. The description 
of the whole will employ some relational word to indicate the 
pattern; what is there, in the non-verbal world, corresponding 
to this relational word? 

The problem is suggested by the distinction between the parts 
of speech. But common language is not sufficiently logical for 
this distinction to be taken over as it stands. We must first 
construct an artificial logical language before we can properly 
investigate our problem. 

Logical languages have been invented by logicians for the 
purposes of logic. They need no actual proper names, since logic 
never speaks about anything in particular. Our purpose is slightly 
different, but by the help of logic we can easily construct the 
sort of language we need. What we require, at the moment, is 
a language that will symbolize, as accurately and systematically 
as possible, all that part of our knowledge which belongs to the 
primary language ; and when we have constructed our language, 
we have to consider what light its structure throws on the 
structure of the percepts in virtue of which its propositions 

are true. 

Our language must, in the first place^ contain proper names 
for all perceived objects which are perceived as units. When 
we perceive a Gestah without analysing it, we must be able to 


name it — e,g. to say "that is a swastika". But when, in geometry, 
we have a figure consisting of several lines, each of which is 
separately noticed, we seem not to need a proper name for the 
whole figure. Nevertheless, if there is such a thing as a judgment 
of analysis, where the analysis is of the sort we have already 
considered, i.e. of spatio-temporal whole and part, it needs a 
proper name for the whole and other proper names for the parts. 
Suppose, for instance, you want to say, not in general, but in 


a particular case, that a certain face consists of its two eyes, its 
nose, and its mouth (ignoring other parts), you will have to pro- 



ceed as follows : Let us call the face F, the eyes respectively E 
and Eg, the nose N, and the mouth M. Then F consists of E 
N, M arranged so that Ei and E2 are ovals on a level, N is a 
narrow isosceles triangle which descends vertically from half way 

between Ei and Eo, and M is a horizontal line with its middle 

point vertically below N, (This is not a very accurate descrip- 
tion of a face, but is suffices to illustrate linguistic necessities.) 

will be seen that F, here, seems somewhat superfluous, 
since the state of affairs can be described completely by means 

of El, E2, N, and M. Whether there is or is not any need 

for the proper name "F" is a question which, for 
the moment, I will leave open. 

In the above description of a particular face, 
we have had to use other words besides the 
proper names. We have had to state the spatial 
relations of the parts. Let us simplify the matter by reducing 

the eyes and nose to lines. Then we may say: E^ and Eg are 

equal parts of one horizontal line; if Eq is the middle point 
between Ei and Eg, N is part of the vertical line descending from 
Eq, M has its middle point on this line, and is part of a horizontal 
line below N. This statement has a geometrical accuracy which 
is lacking in perception, but that is not important at the moment. 
We can perhaps, in the visual field, take "horizontar* and 
"vertical" as predicates, like "blue" and "red". But we need 
statements such as "E, is to the left of E2", "Ei is above N", "' ' 

is above M". There is no possible way of describing what we 
see without relational statements of this sort. 

Let us consider this from a scientific point of view. Complete 
information about the visual field at any moment would consist 
of propositions stating the colour of each place in it. The visual 
field has an absolute origin, the poicit upon which we are focus- 
ing, and absolute position in the field is defined by two angular 
coordinates, which we may call fl, <f>.* Thus the visual field is 

♦ I am, for the sake of simplicity, ignoring depth as a visual quality. 


completely specified if we know, for a variable x which may 
take all values that are shades of colour, the value of x that 

for every Q and <^, where *y*(&, ^)" means "the shade of colour 

at (5, ^)'\ This is a triadic relation between x and Q and ^, and 

it does not seem possible to describe the visual field more simply* 
Let us consider the following sentence : "as I was leaving the 

theatre, I heard cries of *fire' and was violently pushed by a 

panic-stricken mob." This cannot quite report a judgment of 
perception, for "panic-stricken*^ is hardly a quality of perceptible 
data. But we only have to omit the words "by a panic-stricken 
mob" to have a possible judgment of perception. What, exactly, 
does it assert } It asserts the simultaneity of the following three 
percepts: (i) my visual field was such-and-such (what in fact 
it is when one is close to the exit); (2) I heard the sound "fire" 

repeatedly; (3) I experienced a strong sensation of pressure in 
the back. We may simplify this, and substitute the simultaneity 
of the following: (i) I saw and felt my hand touching the door; 
(2) I heard the sound "fire"; (3) I felt a violent pressure of the 
sort that one refers to the back. Here a visual, an auditory, and 
two tactual data are said to be simultaneous. The word "simul- 

taneous" is difficult, but I think that, when we are discussing 
data, it means "parts of one perspective experience". And when 
A, B, C, D are simultaneous, that does not mean merely that 
A and B, B and C, C and D are simultaneous in pairs; for any- 
thing perceptible lasts for a finite time, and therefore simultaneity 
among perceptibles is not transitive. Thus in our case there must 
have been one experience, or, in a sense, one perception, which 
embraced the visual, the auditory, and the two tactual data. 

may be said that the simultaneity of a number of events 
can be inferred from their all having happened at the same time. 
Let us look into this. A watch or clock is {inter alia) a device 

for giving names to a number of very brief events. Let us suppose 
a clock which indicates not only seconds, minutes, and hours, 




but the day of the month and the month of the year. We may 
even let it indicate the year. In that case, such-and-such an 
appearance of the clock is an event which lasts for exactly a 
second and never recurs. Let us suppose that you are such an 
expert in perceiving Gestalt that you can distinguish any two 
different appearances of the clock without having to notice the 
separate hands. You can then give the proper name "A" to the 
appearance of the clock at exactly 1045 p.m. on December i, 
1940. You may observe successively, concerning the events 
B. C, D, E, that B was simultaneous with A, that C was so, 

> ^> ^'> -^y 

that D was so, and that E was so; but you cannot infer that 
B, C, D, and E were simultaneous with each other, since they 

may all have been very brief; they might, for instance, have been 
the four words "fly for your lives", which can easily be uttered 
successively in a second 

now, your clock, instead of changing its appearance only 
once a second, changes it as often as is compatible with the 
perception of jerks rather than continuous motion, you will be 
unable to make successive observations while its appearance 
remains unchanged, and therefore you cannot know that two 
events were both simultaneous with one appearance of the clock 
unless they and this appearance were all parts of one experience ; 
and when I say that they were parts of one experience, I mean 
that there is a perceptive proposition in the primary language 
which asserts their togetherness or simultaneity. The clock, 
therefore, however elaborate, does not help us out. We must 
admit that we can perceive several events as simultaneous, and 
obviously there is no theoretical limit to the number of such 


What follows from the above is that we must allow, widiin 
the primary language, for the possibility of /i-adic relations, 
where n is any finite number. There must, that is to say, be 
words which are not proper names, but predicates, or dyadic 
relations, or triadic relations, or etc. 

What has been said so far in this chapter is preliminary to the 

question, which, as already stated, is this: can we state all 






that we know without the use o( any basic prt:>{7i>sitions of the 

form **P is part of W? In asking this questiim, ii is supposed 
that **P" and **W'' are proper names* It will be remembered that, 
in Chapter VIII, we concluded thai nil judj^inenis of perception 
are of this form, and that what, in such pri^positions, we naturallv 
call **this*\ is a complex which die judgnieni ot perception par 
tially analyses. It is assumed, in saying tliis^ that we can expe 

rience a whole W wittiout kmnving what its parts are^ but that, 

by attenricn) or noticing^ sw can gradually discover more and 
more of its parts, it is not assumed that this process musi 
short of complete analysis, mir is h assumed thai it can be carried 

to the point at wliiclt ilie pans tfjat liave been arrived at are 

incapable of further analvsis. But it is assumed that liie wh«)!e 


can preserve its identity t!iroug!u:nu the process t»f analysis: ihat^ 
e*g,, in perceptit^n we can I.H\uin with **W!'' as an exclamatory 

use of an object-Wijrd, and arrive^ by atieniiun, at **P is part 
of W\ \vit!H,.5Ut any ciiange in the deuinaiiiHi r^f t!ie nanu* **W*\ 

the above accinint there is a suggestion iif a chronological 

process of analysing, which is perhaps m)l Uigically essential to 
the theory that names fi»r wholes are tndisnensabte, Wlien we 


study a perceptual datum* which, at tirsi, appears as a vague 
wholcj we may gradually arrive at an enumeration i>f interrelated 

parts; but ir^ sucli a case it may be said thai the iUmm changes 
as a result of attention. Hiis is certainly true, for e,\ampk% in 

the case of a visual datunt which we i^bservt* first carelesslv, and 

then atieniiveiy* Attention, in sucfi a case, invi4ves changes in 

the eyes, which change t!ie vistia! object* Ii may be saiti that all 

analysing is of this sort, and that the whole whose parts are 

kmnvn is never identical with the privitni^ wlu^le uhich was 
perceived vaguely. I do not think it is necesnary for t\w ilteory 

we are considering liJ deny this. We can, I thinks cunfine tjur- 
selves to t!ie finished product of tmr analy^mi^ ^nnl a-^k ourselves: 
can this resuh be expressed witlnnn referiitee to whtde-and- 
pari i 


Our question is: when we S pert,etve that a whtjle has pans 


do our data ahvays consist of propusiiions abinit the parts and 



their relations^ or must they sometimes contain propositions in 






mentioned? This is again the question of 


ConsidcT (say) a circle, which 

we will call A. and a 

siraight !ifH% L, whicli passes through it. We can say **L divides 

A intu fwu intrH 

K » 

but we mav be 

in A as a whole 


and in the fact that it is divided^ without being in the least 

for instance, a thin 

iriteri*sied in ihe srpurait* pans. Ccm^ider^ 

cicmd cuiiin|j': die full mmm in nvih We remain aware of the 

mmm as a 





muchanMre vividly ilian of the parts. 

Or wnnider a Hiiniewhiif ciitiereni case. We see a distant object 

appriiachiiitf. alan}i; a raad; ai Itriit we &Bfy see it 

as a whole, but 

gradually we sw n nearly enough lo make out that it is a dog 

When tixh happens, 0ur visual object is of course, not the same 

a*» ii was k*fare, hut we k^lieve it m be connected with the same 



ijeei, whieh ha^, fram ihe firHi, interested us as a whole. 

fence wlien we mnw la H*e ihe 

we see them as parts, not 

as 5»c*paraie items arranged in a ceriain pattern 

to me 

that, in !^uch a 

whai we 

sereeive cannot be accurately ex- 

witlitiui priiptniiians of the form 


is part 

of W 







are preiper name*» 



, and P, at 

ka*ifi is unly pan *:*f uur luial percept 


i$ lake antnher in?»iana* 

a e 

hild who is being tau 


modern nie«ht)d.H, m read the won 







"a", "f" 

earns to make, in 
the sounds these 

iucce^^it;in, me stmnas k ^ a ^ i . \i nmmu ui^- »^w««^« *•*— 

hmt% mnd Un, nm the name^ of ilie letters,) At first, the interval 



between the sounds is too long for the child to be conscious 
of their succession as forming a whole, but ar last, as the rapidity 
increases, there comes a moment when the child is aware of having 
said the word *'cat*\ In that moment, the child is aware of the 
word as a whole composed of parts. Before that, he was not 
aware of the whole; when he can read fluently, he ceases to be 
aware of the parts; but in the first moment of understanding, 
whole and parts are equally present in consciousness* Wliat the 
child is aware of in this moment cannot be eKpressi!d without 
such propositions as **the sound *k* is part of the sound *cai* * 

think that all judgments of perception involve analysis of 
a perceptual whole; what is given is a pattern, and the reali:£aiion 
that it consists of interrelated objects results imm analysis. With- 
out propositions of tlie form **P is pari of W**, the process would 
not be explicable. It seems, ihereforei that such propositicms must 
occur in the primary language. 

Every judgment of perception which contains more than one 
object- word expresses an analysis of a perceived complex whole; 
the perceived whole is^ in one sense^ known by tx*ing perceived, 
but the kind of knowledge which is opposed to error requires 
something more than perception- A judgment of perception which 

contains more than one object* word^ and is expressed in a sen- 
tence which is not equivalent lo several separate sentences^ must 

contain at least one word of which the meaning is reiaiional 
There is no theoretical limit to the complexity of the object of 

perception or of the structure affirmed in judgments of perception 
which the object verifies. It is upon the complexity of the 
of perception ihai our knowledge of b*-iib space and time 

Assuming^ as it seems from the above tliai we must, that there 
are wholes composed of interrelated parts^ and thai the know- 
ledge expressed in judgments of perception recjuires, for its 
verbalization* names for such wholes, there remains a difficult 

question* namely: in what circumstances do inierrelaied terms 

form a whole> which needs a tmm for the verbal expression of 
what we know ? 

The argument demands that the total of our acperience at 



any one time should always be such a whole, and so must certain 
complex parts of this total The parts of such a total are boui\d 

together by the relation of compresence- For reasons explained 
in Chapter XXI, we hoid that the relation of compresence may 

as well as within it : indeed, if there is 

> •*'^^^^> 

hold outside 

the unexperienced world that physics supposes, its space-time will 
depend upon unexperienced compresence* Perhaps wholes, of the 
indispensable son, are always constituted by compresence. Let us 

examine this posHibiliiy 
In the following pages^ I shall be concerned to develop a 

possBk view on the element of analysis in Judgments of per- 

am nm concerned to maintain that this view is 

Lei us give the name **W*' to my total perceptual field at 

5iome fi;iven m<*mi*ni. At $hm moment, I can give the pseudo- 

*'thiH** to W, and also to certain parts of W, but not to 
anything brgcr dian W. The pseudo-name *i-now** applies to 

the whole of W at the moment when W exists, and not to any 
part of W. According to the theory of Chapter VI, W is a bundle 

of compre»ient cjualitits* To these qualities we can give names 

Let *'Q'* be the name c5f one of them. Then **I-now perceive Q** 

is to be iranstaied into **Q is part, of W 


is tu im satisfactory^ it is necessary that, among the 

qualities coniiiiniiing W, there should be at least one which does 

not recur, or one subordtnaie complex which does not recur 

For the %ake of simpliciiy, I shall suppose that I am always 
watching a c!f>ck which indicata not only minutes and hours, 
but the day of the month, the month of the year, and the 

year of our Lord* If now I give the name **^'* to the aspect 

of ihii clock which h pan of W, 'V wit! designate a group of 

ciualities which has m temporal relation to itself, U. occurs only 
once. Any other aspect of ihe clock will be earlier or later than *, 
and we shaill »ay that the total perceptual field of which this other 
a'$pcci is a part is correspondingly earlier or later than W. 

lo the above, the values of t form a numerically 

scries, and two different values of t cannot be com 



present unless they are so nearly equal that they can be parts of 
one specious present, i.e. of one W. All this is empirical. 

We now have to consider what parts of W can be wholes 
requiring names for the expression of judgments of perception. 
The total W may be analysed into a number of qualities, but 
this analysis will not, by itself, enable us to explain such 
judgments of perception as "A is to the left of B". These demand 
the analysis of W into what we should be tempted to call "sub- 
stantial" rather than "conceptual" parts. They demand, that is 
to say, an investigation of spatial analysis within a given per- 
ceptual whole. 

Let us again, as on former occasions, confine ourselves to the 
visual field and ignore depth. We may then say, with a simpli- 
fication which is innocuous, that there are in the visual field a 
number of differing qualities of up-and-downness and a number 
of differing qualities of right-and-leftness. Any one of the former 
we will denote by "5" and any one of the latter by * V". Apart 
from differences in excellence of vision, we may suppose that 
each quality 6 and each quality ^ exists in everybody's field of 
vision whenever his eyes are open and it His not dark. 

We now require a relation of "overlapping", which plays a 
part in the construction of perceptual space analogous to that 

played by compresence in private time. I do not define this 
relation, but I maintain that, if Q and Q' are two qualities, "Q 
and Q' overlap" can be a judgment of perception. For example: 
red and bright can overlap; so can a given degree of pressure 
with the quality by which we distinguish a touch on one part 

of the body from a touch on another. Two different ^-qualities 
cannot overlap; no more can two diflferent ^-qualities. Two 

different colours cannot overlap; no more can two touch- 
qualities belonging to different parts of the body. Any visual 
quality can overlap with any and with any <f>. 

Two different valuea of d have to each other an asymmetrical 
spatial relation, that of above or below; two different values of 
^ have an asymmetrical spatial relation, that of right or left. A 
given value of d will have a relation of right or left, but not of 





Up or down, to itself, and a given value of <}> will have a relation 
of up or down, but not of right or left, to itself; a complex (?, 


will have no spatial relation to itself. This fact is what 
trying to express when we say that it can only occur once in 

a given visual field. 

If, now, a given quality, say a shade of colour C, exists through- 
out a region of the visual field, that means that it overlaps with 

many values of the pair of qualities (6, (j)). Since 9 and <^ are 
numerically measurable, we can define straightforwardly what 
we mean by a "continuous" region in the visual field. Similarly 
we can define regions in tactual space. What we should commonly 
regard as a "substantial** part of the whole W is any continuous 
region which is part of W. Any such region may be a "this" 

When we say "A is to the left of B", we may take "A" to 
be the name of the complex consisting of given values of 9 and <^ 

together with all the qualities overlapping with both, while 
is similarly defined for other given values of 6 and <l>. Our state- 
ment is to be true if the A-value of <^ is to the left of the B-value. 
Thus in "A is to the left of B*' the whole W does not need 

to be mentioned. But if this sentence expresses a judgment of 

perception, there must' be a whole W of which A and B are 


We may now reach a conclusion as to names. The primary 
names are those applying to such wholes as W, or to continuous 

regions which are parts of some W. Other names are derivative 

and theoretically unnecessary. 

It will perhaps help to make clear the scope of what has been 

said if we proceed to the construction of physical space-time. 

In this construction we necessarily assume the truth of physics. 

Space-time in phvsics is elaborately inferential, and is con- 
structed largely by means of causal laws. It is assumed that, it 
there is a causal law connecting two events at different places 
in space-time, they are connected by means of a chain of events 
at intermediate places. The physical and physiological causation 
of percepts compels us to regard them as all in one region, which 
must be inside the percipient's head (not, of course, mside his 



or any one else's percept of his head). The relation of com- 
presence^ which exists between percepts, may be supposed to 
exist also between any two physical events which overlap in 
space-time. A "point*' in space-time may be defined as a group 
of events having the following two properties: (i) any two of 
e group are compresent; (2) nothing outside the group is 
compresenc with every member of it* 

The ordering of points in space^time is by no means a simple 
matter^ as Einstein has shown* It begins, hisiDrically, from the 
belief that every percept is **of*' some physical obfect^ and tliat 
tiie order of the physical objects in physical space is correlated, 
somewhat roughly^ with that of the corresponding percepts in 
perceptual space. The angular coordinates of stars in physical 
space are very nearly the same as those of their percepts in visual 

space. But the notion that a percept is **of'* a piiysical object 

, ^^v««,v*.^ 

turns out to be inexact, causal and unreliable. The more exact 

determination of space-time order depends upon causal laws: 
e.g* the distance of Jupiter is calculated from observations which, 
assuming the law of gravitation, enable us 10 calculate how loniG! 

ight has taken to travel from there to us. 

There is no need to pursue this matfer further. The imptir* 
tant points, for us, are t%vo: that my perceptual whole W is> from 
the standpoint of physics, inside my head as a physical object; 
and that space-time whole and part is too elaborate and inferen- 

tial a concept to be of much importance in the foundations of 
theory of knowled 


Chapter XXV 


In the present chapter I propose to consider whether anything, 
and, if so, what, can be inferred from the structure of language 


to the structure of the world. There has been a tendency 
especially among logical positivists, to treat language as an inde 


realm, which 

can be studied 

without regard to non- 
To some extent, and in a limited field, 


linguistic occurrences 

this separation of language from other facts is possible 
detached study of logical syntax has undoubtedly yielded valu- 

think it is easy to exaggerate what can be 



able results 


achieved by syntax alone. There is, I think, a discoverable relation 
between the structure of sentences and the structure of the occur- 
rences to which the sentences refer, I do not think the structure 

believe that. 

of non-verbal facts is wholly unknowable, and 

with sufficient caution, the properties of language may help us 


understand the structure of the world. 

With regard to the relation of words to non-verbal facts 
philosophers can be divided into three broad types 



Those who infer properties of the world from properties 
of language. These are a very distinguished party ; they include 

Parmenides, Plato, Spinoza, Leibniz, Hegel, and Bradley. 

„. Those who maintain that knowledge is only of words. 

Among these are the Nominalists and some of the Logical 

Positivists. . , , 

Those who maintain that there is knowledge not expres- 

use words to tell us what this knowledge 

is. These include the mystics 

certain aspects of Hegel and Bradley 

sible in 

words, and 

Bergson, and Wittgenstein 


Of these three parties 


the third can be dismissed as 





contradictory. The second conies to grief on the empirical fact 
that we can know what words occur in a sentence, and that this 
is not a verbal fact, although it is indispensable to the verbalists. 
If, therefore, we are confined to the above three alternatives, we 
must make the best of the first. 

We may divide our problem into two parts: first, what is 
implied by the correspondence theory of truth, in the measure 

in which we have accepted this theory ? Second, is there anythin 
in the world corresponding to the distinction between 
parts of speech, as this appears in a logical language ? 

As regards ^^correspondence'*, we have been led to the belie 

that, when a proposition is true, it is true in virtue of one or 

more occurrences which are called its ^'verifiers**. If it is a pro- 
position containing no variable, it cannot have more than one 

We may confine ourselves to this case, since it involves 
the whole of the problem with whicli we are concerned* We 
have thus to inquire whether, given a sentence (supposed true) 
which contains no variable, we can infer anything as to the 
structure of the verifier from that of the sentence. In this inquiry 
we shall presuppose a logical language* , 

Consider first a group of sentences '^diicli all contain a certain 
name (or a synonym for it). These sentences all have somethin 
in common. Can we say that their verifiers also have sometliin 

m common 


Here we must distinguish according to the kind of name con 

If W is a complete group of qualifies, sucli as we con- 
sidered in the last cliapter^ and we form a number of judgments 
of perception^ such as **W is red**, *'W is raund*\ **W is ki 

eta, these all have one single verifier, namely W, But if I make 

a number of true statements concerning a given shade of colour 


they all have different verifiers. These all have a common 

part C, fust as the statements have a common part **C'*. It will 
be seen that here, as in the last chapter, we are led to a view 

__ ^^^„^ ™.,«„^^ p.»^«Y^ WW «»«» «r#A^ mm^^ qM»««lM|#«t««^,ft4^ T¥%« m^^m #%<Vi ^%^ W V ft V W 

which, syntactically, is scarcely distinguishable from the subject- 

predicate view, from which it differs only in that it regards the 

subject" as a bundle of compresent qualities. We may 



what has just been said as follows: given a number of subject 

predicate sentences expressing judgments of perception, such as 

this is red'*, if they all have the same subject they all have the 
same verifier, which is what the subject designates; if they all 
have the same predicate^ the verifiers all have a common part 
whicli is %vhat the predicate designates* 


theory is not applicable to such a sentence as "A is to 

e left of \V\ where **A** and "B'' are names for two parts of 

my visual field* So far as **A" and "B" are concerned, we con 
sidered this sentence sufficiently in the last chapter. What I now 
wish to examine is the question: what, if anything^ is common 
to the verifiers of a number of different sentences of the form 

**A is to the left of B"? 

The question involved is the old question of **universal$". 
We might have investigated this question in connection with 

predicates— say **red is a colour*', or *lHgh C is a sound**. But 

since we liave explained the more apparently obvious subject 
predicate sentences-'— e.g. **tlus is red" — as really not subject- 
predicate sentences, we shall find it more convenient to discuss 
**universaLs** in connection %vitli relations. 

Sentences— t*xcept oL'ject-words used in an exclamatory man- 
ner—require words otlier than names. Such words, generically, 
we call **re!atton-words*\ including predicates as words for 
monadic relations. The definition, as explained in Chapter VI, 
is syntactical: a **name** is a word which can occur significanriy 
in an atomic sentence of any form; a "relation- word" is one 

which can CKCur in some atomic sentences, but only in such as 

contain the appropriate number of names. 

It is generally agreed that language requires relation-words 


the question at issue is: **what does tius imply as regards the 

verifiers of sentences?'* A **universal'* may be defined as **the 
meaning (if any) of a relation-word". Such words as *1f '* and 

**or** have no meaning in isolation, and it may be that the same 
is true of relation-words. 

may be suggested (erroneously, as I think and shall try 

to prove) that we need not assume umversals^ but only a set 



of Stimuli to the making of one of a set of similar noises- The 

matter is, however, not quite straightforward, A defender of 
universals, if attacked, might begin in this way: **you say that 

two cats, because they are similar, stimulate die utterance of two 
similar noises which are both instances of the word 'cat\ But 
the cats must be really similar to each otiter, and so must the 
noises. And if they are really similar, it is impossible that *simi- 
larity* should be just a word. It is a word which you utter on 
certain occasions, namely, when there is similarity. Your tricks 
and devices*', he will say, **may seem to dispose of other univer- 
sals, but only by putting all the work on to this one remainin 
universal, similarity; of that you cannot get rid, and therefore 
you might as well admit all the rest/* 

The question of universals is difficuh, not only to decide, but 
to formulate. Let us consider **A is to the left of IV\ Places in 
the momentary visual fiekl^ as we have seen, are absolute, and 
are defined by relation to the centre of the field of vision* They 

may be defined by the two relations right-and-left, up-and 
down; these relations, at any rate, suffice for ti>pokif2;icaI purposes 
In order to study momentary visual space, it is necensary to keep 
the eyes motionless and attend to things near tlie peripliery as 
well as in the centre of the field of vision- If we are nm de 

berately keeping our eyes motionless, we shall kmk directly ai 
whatever we notice; tiie natural way m exatBine a series <if p 
is to look at each in turn. But if we want to stuiv what we can 
see at one moment, this method wi!! mn du, since a given physical 
object, as a visual datum, is different wlien it is seen directly and 
when it is far from the centre of the field. In facr^ however^ iliis 
makes very little difference. We cannot escape from the fact that 
visual positions form a two-dimensional series, and that such 

series demand dyadic asymmetrical relations. The view we take 
as to colours makes no difference in this respect 

seems that there is no escape fn)m admitiinu relations as 

parts of the non-linguistic constitution of the world; similarity 

and perhaps also asymmetrical relations, cannot be explained 
away, like **or^' and **not*; as belonging only to speech. Such 

'It (T.^ — 

V\"i f 

IL "• 



mxds as **before'* and **above'^ just as truly as proper names 

mean" something %v!nch occurs in objects of perception 
:>llows that there is a valid form of analysis which is not that 
f whole and part. We can perceive A-before-B as a whole, but 
we perceived it oniy as a whole we should not know whether 

/e had seen it or B-before-A. The whole-and-part analysis of 
he datum A*faefore-B yields only A and B, and leaves out 

therefore, there will be some 

*betare". In a 

iistinctions of pans of speech which correspond to objective 


Let us examine once more t!ie question whether asymmetrical 

relations are needed as well as similarity; and let us take> for 

he purpose, **A is above B*', where **A*' and **B'* are proper 

!iames of i^vmn. We shall suppose that we perceive that A is 

above B, N<nv it h clear^ to l>egin with a trivial pointy that we do 

mn med die wurd **below*' as well as the %vord **above**j either 
aione suffices. ! shjiU therefore assume that our language contains 

no word **below*\ The whole percept, A-above-B 


r percepts C-above«D, E-above-F, etc. in a manner which 

J •«, ^^^,^ * , >.w^ 

make?* us call rl^^m all facts of vertical order. So far, we do not 

need a concept **above*' ; we may have merely a group of similar 

occurrences^ all called **vertica! orders'*, i.e, all causing a noise 

similar lo **above**'* So far, we can do with oniy similarity 

But now we nnmi consider asymmetry. When you say **A is 

above iy\ lunv does your Iiearer know that you have not said 

**B is above A'*? In exactly the same way mym know that A is 


above E; he perceives that tlie noise **A'* precedes the noise 

Thus the vital matter is tlie distinction between A*first-and 

ihen-B^ B-first-and-ihen*A;orj in writing, between AB and BA* 

Consider^ liien^ the two following shapes: AB and BA« I want 

to make it clear that I am speaking of just these^ not of others 

them* Let S| l>e the proper nmm of the first shape^ S^ that 

of the second; lei A|^ A^ be the proper names of the two A*s, 

and B|^ B| of the iwo B*s* Tlien S|^ S| each consist of two parts 

and one part of S| is closely similar to one part of Sji, while the 

ottier pan is closely similar to the other part* Moreover;^ the 























f i 










9 I f 




■! f 





ordering relation is the same in both cases* Nevertheless^ the 
two wholes are not very similar. Perhaps asymmetry could be 
explained in this way: given a number of A*s and a number of 
B*s, arranged in pairs, the resulting wholes fall into two classes^ 
members of the same class being closely similar to each other^ 
while members of different classes are very dissimilar* If we give 

the proper names S^, S4 to the following two shapes: AB and 

BA, then it is obvious that Sj and ^ are very similar, and so 

are S^ and S4, but S^ and % are not very similar to S^ and S 


(Observe that^ in describing $1 and S^^ we shall have to say 


I consists of Aj before Biy S^ consists of B^ before A^-) Perhaps 
in this way it is possible to explain asymmetry in terms of simi 

larity, though the explanation is not very satisfactory. 

Assuming that we can, in the above manner or in some other 
get rid of all 


similarity, it remains to be con- 

sidered whether similarity itself could be explained away* 

We will consider this in the simplest possible case* Two patches 
of red (not necessarily of exactly the same shade) are similar, and 

so are two instances of the word **r€d"» Let us suooose that 

we are being shown a number of coloured discs and asked to 

name their colours — say in a test for colour-blindness* We are 
shown two red discs in succession^ and each time we say **red^*. 

We have been saying that, in the primary language, similar 

stimuli produce similar reactions; our theory of meaning has 

been based on this. In our case, the two discs are similar^ and 

the two utterances of the word **red** are similar. Are we sayin 
the same thing about the discs and about the utteranca when 
we say the discs are similar and when we say the utterances are 
similar? or are we only saying similar things? In the former case, 

if A and B are perceived to be similar^ and C and 

similarity is a true universal; in the latter case^ not. The difficulty 
in the latter case, is the eiidless regress ; but are we sure thai this 
difficulty is insuparable ? We shall say, if we adopt this alterimtive: 

are also 

perceived to be.similar, that means that AB is a whole of a certain 
kind and CD is a whole of the same kind; i*e*, since we do not 
want to define the kind by a universal, AB and CD are simiim' 





do not see how we are to avoid an endless regress of 
vicious kind if we attempt to explain similarity in this way- 
conclude, therefore, though with hesitation, that there are 
versals, and not merely general words. Similarity, at least, 

have to be admitted ; and in that case it seems hardly worth 
:iile to adopt elaborate devices for the exclusion of other 

It should be observed that the above argument only proves 
e necessity of the word "similar", not of the word "similarity". 

Some propositions containing the word "similarity" can be 
placed by equivalent propositions containing the word "simi- 
"* Tvhile other cannot. These latter need not be admitted. 


uppose, for example, I say "similarity exists". If "exists" means 

/hat it does when 


the President of the United States 

my statement is nonsense. What I can mean may, to begi 




pressed in the statement 

there are occurrences 

vhich require for their verbal description sentences of the form 
n is similar to * ' ". But this linguistic fact seems to imply a fact 
Jiout tlie occurrences described, namely the sort of fact that is 
asserted when I sav "a 4s similar to i". When I say "similarity 




say "a 4s 
, it is this fact about the world, not a fact about language, 
mean to assert. The word "yellow" is necessary because 

here are yellow things ; the word 


similar' ' is necessary because 

there are pairs of similar things. And the similarity of tw^o thing 

truly a non-linguistic fact as the yellowness of one thing 

IS as 

We have arrived, in this chapter, at a result which has been 


in a sense, the goal 

of all our discussions. The result I have in 
mind is this : that complete metaphysical agnosticism is not com- 
patible with the maintenance of linguistic propositions. Some 
modern philosophers hold that we know much about language, 
but nothing about anything else. This view forgets that language 

IS an 

empirical phenomenon like another, and that a 


is metaphysically 

gnostic must deny that he knows when he 

uses a word. For my part, I believe that, partly by means of the 
study of syntax, we can arrive at considerable knowledge con 
cerning the structure of the world. 
















All", 19 f^, 46 f*» <^4» 74 U 78 f'> S^ ^• 

93 f.> X47 ^", 3:64> 280, ^98 

Analysis, 19 ^-j 


Cartesiamsm,i6, 1x6 f., 13 ^M3 ^ 
Causal Law, Causation 


24, 166 Lj 189^ 






160, 220, Z33 £. 




Assenibility, iS9f.»3iS^ 

cf. Dewey 

M4f ^^h 3J<^> 324> 339 

Certainty, x8, X03, n7> i^4> ^33 


Associatian, 51 f., ^7> 7of 






3x6 £ 


iS> 35, 3S> <S8 




3Sfn 4^^' 



344 f' 

cf. Symmetry 


cf. Hegel 

Atomic form, 34* 44 U ^>% 95, ^M, ^^^ 

Atomic proposition 




j<>3, a<3<> 

cf. Molecular proposition 

Atomic scmenoi, 31 f», 45, *^3> ^95 ^• 


199, 291 


A warencss» 1 3, 228 f 

c£ Molecular sentence 
m U 20Z f., 259 f'> 3^7 f' 



Class, Classification, 

229 f., 3^3 
Coherence, 140, x^^, 

Combination, 195 f., 202 

Common sense, xi<5f., X39, 223, 234, 

145, ^99, 3<5i ^ , 

Complex, Complexity, 56, 267, 272 

Compresence, 1x4, ^^7, ^^7> ^3^>M^ 

301, 337 f'- 
Conjunction, 30, 41, 4<S, <>4, S99 




I *> 1 7, X 37- cf * Positivists 

Basic proposition, X7£, 82 f., 88, 92 
137 f., isot 
143 f- 

Constant, 26$, 3<>9 
Copilowish, 184 f. 
Correspondence, 2 

cf. Variable 






62 f., 226; 237 £ 



89 f., 3<5i> 3c>S» 341 


89 f 

cf. Proposition 

Behaviour, Behaviourism, i4>»*', ***4*' 

248 f., 262, 297 
Belid; Iklieving, 16 f., 21, 65, 94 


Dalkey, Mr. N., 7, ^7^ 

Data, Datum, 124 £, i^5, i93, 334 

$32, 138, J<S7, 17X, 1^75^' 
103, 207 £*, a*«>f*> i»9«' 



190 f. 
223 f. 

Dewey, Prof. 




89 £ 

3x8 f. 





22<> S», »35 «*» ■ 

294, 298, 32 X f 

247 £, 159 f-T 1^9 f' 

Disjunction, 83 £, 86 £, 90 f-, X99> ^" 

Doubt, x<S, x8, 21, 65, 94, * ^7, 3^3 *- 



Bergson, xoi, 
Berkeley, 7> 

a37t 3x5 

Broiiwer, 21, 274 £ 

eluded Middle 

c£ Memory 



2x7, 133, 






c£ Law of Ex 

c£ Newton 


Cat'sar, 12, 17. 3«* 33 f- 

36 £ 



16^, 172, J79, «*^i f-* *^» **'7, iS<^» 

266 f., 325 

26 £., 23 X f . 

Einstein, 320, 340* 
Empirical, Empiricism, 18 

45 f., 5^, 57 1%<50, 91 f. 11*5,135^: 

65, 2x7 U ii<5, 232, 239, 158 





274, 298, 305 £., 314 

89 f 

Catnap, 7 


x8, 23, 4»f ^if'» 93, 

42 f 

48, *59f 



(^7^-, 175 f" 


c£ Phy 

H umber 

Error, 14, »<>> *^^ 

Event, xox, 



279 f 


239, 288, 304, 3^9, 

324 £ 




. ?■ 


Existence, 6$, zt% ^37 f., 242 f.> 254, I Indication, 1 

171, 204 f. 

2g6, 303f., 310, 347 

Experience, rj, 17 £, 40, 48 t, 53 f,, 



<k>, 80 £ 


izt £ 




236 £, ^43, Inducdon, 76 



279 f., 2^1 £> 29s f" 

2Sif., 287, 303 f-» 3 «S 





Expression, xx £., 52, 70 f., 77, X71 


204 £ 


2x4 £ 


Z2r £, 23d, 240 £ 


25a £, 269 £, 291 £ c£ Indication 

Extensionality, 1 6$ £, 259 £ 

Inquiry, 3 19 £ 

22i$ £, ^42 £, a87, 303 





70 £ 


20s £ 




^Wff^Bp^H fl " 

Intention, 53 
Interpretation, 184 £, 323 £ 

^ J IMS ^ ^ ^ 

ism, 1 23 £ 

53 ^*» «>x 


64 £, X ! 2y 20B 

284 £, 289 £, 293, 305 

Factual premiss, 150 £, 232, 2$4, 31s ^. Judgment, 73, 83, 90 £ 




J 19 


c£ Premiss 
False, Falsehood, 19 £, 2^, <>2 £^ 75 £ 
7$£, 81 £, 167 If I7<S£, 187^ Z06 

iS$t tr7, *Si £^ 194* ^3^^ *4I, 2S4* 

|o8£, 31^1, 330, 334 £, 337 £, i4x 

200 £ 

¥ *'f 

2x4 £» 

223 £ 






307 £, $itt, 320 £, 325 

Family, 25, 229 £ 
Function, 64^ 200, 260 £ 

Kaplan, 1 84 £ 

Kepler, 17, 132*297 

Knowledge, n, 20, 48 £# tt6t^ 123 £ 

Generality, Generalization, 88 £^ 92 

34* f 

143, 23^ £ 


287 £ 


a9^» 3X| 




19^ £, 202 £, 254, 259, 2<S3 £, 1716 £ j language, 11,19 £, 23 £, ^2 £, 72, 75, 

Gmait, $(S, S9» 73» Bo> 133 
Gddel, 7* f. 
Gravitation^ 17, 131, 320 

78 £, 94, I74t m^ 3i«>»^*f *S4> *<^3 













c£ Qb}ect4;»nguage, Primary kn* 

Habit, t3, 47| 121, 137?^ ^S4» 207* t Law of Contradiciioni 19S, 259, 274£ 

244, 247 £, 253, 296 £, 309 £ 
Hegel, Hegeliaurusm, 123 £, 140, 2S9, 

law of Exckidt'd 

34 X 



2S9» 3t74f- 




S72» 19! 


* # 




Hempel^ xi^fn ^47 f* 

X08 £» 231 


Lie> 28, St £, 174, 199 « 204 £| 109,, 
Logic*, 16, 30, 29, 40 £, ^$ £, 64^ 72 


Heiitsitlony 84 £y 2x0 


19 £ 


2«$» <J2 £| 79, 197 £ 

History, X7» x<^2 

Hume, 7y ^21, 191^ 207, 244^ 294^. 3^S 


78 £, Si £# l<S, I ji| 140^ 157^ tM £ 

197, 244, 247i »5^i »5f f*? 31^4 f»> »'74 



277, 2' 






*T*, 20, 9<$, X08 £» 1x3^ 14(5, 231 £ 

I-now**, 108 £» X14, 127 £| 337 
Idea^ X91 £y 294 

Identity, 102 £, 129 £ 

Image, Imagination, 50 £, 180 £, 241, I Mcm<^ry» 

MatJbematic^v 16, 29, 

Mutiefi ii4£, 234 
Meanlngy ii^ 20, 24 f 


I40» i^8| 197 



2<l t* 




341 £ 

x92| 241 £, 27i» 291 £ 

I joO| 




Impression, x 91, 294 

49 f- 




101 £ 


124 f. 



236, 239 






Metaphysics, 21, ($5, 95, 117, 223, zy , 
274, 281, 307, 341 f. 

Mill> J. S., 7<5, n? 

Molticubr ^proposition, 2(53 f., cf. 

Atomic proposition 
Molecular sentence* 31, 41, 195, 199, 


cf. Atomic sentence 




Name, 32, 94(1, 127, 195, 330, 334 

339, 345 f- cf. Proper name 
Negation, 8i f., 259, 27<» 

N<jurath, 23, 139 f., 145 f. 
Newton, 17* n* i** 297 


Nonsen*ie, Nonstrnsical, t66L^ 170^ 

1H3, S9S» ^^9t *7S 

Not**, 20 1% 4<>, 64 L, 70, 77 f. 

Notice, Noticing, 50 f, 







»^ 259,294 


60, 75, 1 10 1\ 




N«nibtT, 72^ $% cf» Enumeration 

» 2«>> *3 « 

Ob|ei:t4unguajJie, 19;, 25, <S2i 









i,anguaj»e, Primary 


Object«w«rd, 25 f„ 65 f,^ 79 f,, 75!'., 




151, 167, 
ci". Wofii 

I Hi; f 


a^^f., 294 




Objftitve, J 4, 2X, 17 « 

C)r'% 20 f,, 25, ^4 ^*'» 7^\7%, 77 *'»> ^3 *' 
H<»f», 92 £, 9S, 2i«C,, 259, 291, 294 

Dr4?r, t^*^ i9fM |9» ;i40 

Pm, i54fn «^*5 

Pi-irvr, 319^ 

P«;rft*|»i. Prra-piiMn, 10, 5^1, 59, 75, 1^3 


90 fn 

Il6t'., I20f., 1351* 




160 f,t 177, »Bt t, 194, i3^>» «4li M9» 

254* 2Hr«r., pif., |oii» 325, inf., 

117 f.» I43if* 

Phyitwalism, 95, ^49, 2^*2^ a^"*?* ^^7* 

Phy^iv^, IS, 33* 9^» *^7t% «o»t nBf., 







l7Si ««** 




240, xHi\ If?, |oo» 304^'.* 117 f. 

Piiysiology, 67, 119, 123, S78f 

193, 208, 285, 297, 339 
Place, 99 f,, 344 

Plato, 23 f,, 58, 341 


cf. Ay 

7, 2of., 137,289, 315,341 

Possibility, 37, X70, 182 

Predicate, 35, 42 f., 45 f., 86 f., 94 f. 

106, 197, 253, 257, 261 f,, 311 f. 
Premiss, 131 f,, 137, i5of. cf. Fac- 
tual premiss 

Primary language, 19, 63 f., 79 f., 246 
cf. Language, Object-language 

Probability, S35, 245, 289, 318, 

Proof, X06, 236 

Proper name, 20, 25, 32 f., 45, 94 f., 

1 27, 330, 3 34, 345 f- cf. Name 

Proposition, 12, 17 f*, 35,4«»,4^, 5^ U 
57 f,, 64, 82, 86 f., 90 f., J 37 f., 142, 


148 f., 152 f 


1 66 f . 


184, 237 f. 

242 Ly 248 f., 253 f., 259 f», 263 
267 f., 276 f*, 280^ 289, 300 f., 304 f» 

308 £, 3JS^% 319 f. cf, Basic pro 




« * 

Propositional attitude, 21, 65, 84, 94, 

163 f,, 167 f., 259, 262, 291 
Propositional forni, 64 
Propositional function, 64, 260 f, 
Prot<x*ol proposition, 20 L 

IVtJtocol sentence, 144 f- 
PrmoMhati^ tl% 141 f., 147, 152 
PNychobgicai aspects, 18 f,, 22 f., 27 

40, 56 f., 6|f., 84 f», 92, 109, 120, 

ijif., 135, 164, iH9i 


193 i 




247 i 



252 f,, 267, 297, 3^1 f. 

Quality, 98, t02» 128, 162, 230 f., 337 





*4$» aB^i P* 


iH^ <* 


6ii* no 








316, 318 







«. J5 



45 f., 94 f 







221 f., 26! f., 26s, 335, 343 r 



Satisfaction, 323 f. 
Schlick, 307 f. 

Science, 103 f., 117, 131, 331 
Sensation^ 40, 119 f,. 285, 329 

•There", xoS £, 295 

Thing,97£, 315, 3i9f. 

**This", 20, 41, 57, 73, 90, 96 £, 108 £ 

27f-» 173> ^^h ^3 



337 f*' 

Sentence, 12, 19, 29 f*, 41, 48 f., 54 f-, Time, 20, 39, 

<53 f-j 75, 9S^'i ^44> i<56f.j 170 f., | Tractatus^ 6z 

2i4f*, 226 f., 236, 246, 291 f., 307 f., 
310 f., 314 f., 342£., 347 





,67 £ 


True, Truth, xx, 18 f., 22, 26, 48, 52^ 

Sign, 14, 1 84 f . 




170 £., 

206 £., 

209 f», 244, 269, 292, 306 f. 

Similarity, 35, 42, 58, 72, 98, 119, 332 

344 f. 
Socrates, 12, 116^ 174, 181, i9<5, 261 f. 

264 £., 2^8 £ 
'"Some", 19 £., 46 £., 64, 70, 74 £., 78 f. 


88 £.,93 £.,157,247,^91 



Space, 20, 100, X18 £., 228, 284 £,, 302 

Space- time, 33, 9<$£, i 





231, 240, 257, 278, 286 £., 337 £ 

Speech, 26 £, 30 £ 
Spontaneity, 204 £, 212, 215 

Statement, 71 £, 87, 92, 147, 261 £, 301 


52 f 







205, 251, 254, 34<S 

Structure, 34, 341 

Subjective, 14, 22, X7X 
Substance, 33, 97, 129 
Substitution, X95 £ 
Symmetry, 35, 42. c£ Asymmetry 

Syntax, 12, 19 £, 30 £, 34, 41, ^$1 


166 1. i7o£ 



J 94 f-» ^75, 341 

Tarski, (S2 £, 284 

Tense, io8£, 250 

, 57, 73, 9<5£, X08 £> 2X1 

46 £, ($4 



75 f' 


78 £ 


140 £ 



67 £, 176 £, 187,206 

£, 2i4£ 

223 £, 226 £, 236 £, 244 £, 259 £ 
265, 274 £, 284, 287 £, 289 £, 306 £ 
312 £, 3x8 £, 322 £, 342 £ 


Unity, 30 £, 34 £ 

Universal, Universality, 24, 36, 95, jij^ 
343 ^'7 34<> f- 

Variabie, 19, X98 £, 220 £, 23<S£, 24 1^ 
244 £, 260 £, 265, 298 £, 309, 342. 
c£ Constant 

Verifiability, Verification, Verifier, 22^ 
79 £, 222 £, 227 £, 231 £, 238, 242^ 

257, 274 £, 289 £, 303 £, 3 

342 £ 




Whole, 40, X28 £, 327 £, 334 £, 338 i 

Wittgenstein, 25, 62, 102, 142, 168, 

262. i66 £ 

c£ Traaatus 

> »»70, 34«- 

, X2, X9 £, 23 £, 48 £, 53 £, «4 
6Z £, 78 £, 94 £, X08 £, iSx £ 




c£ Object^word 



341 t 

World, i2£, ixx £, X41, 233, 237, 329 


34X, 347 




xoS £, 230